{"id":26870,"date":"2023-03-28T07:24:34","date_gmt":"2023-03-28T07:24:34","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=26870"},"modified":"2024-01-23T12:43:15","modified_gmt":"2024-01-23T12:43:15","slug":"unit-circle-definition-chart-equation-examples-facts","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/unit-circle","title":{"rendered":"Unit Circle &#8211; Definition, Chart, Equation, Examples, Facts"},"content":{"rendered":"<div class=\"aioseo-breadcrumbs\"><span class=\"aioseo-breadcrumb\">\n\tMath-Vocabulary\n<\/span><\/div>\n\n<div class=\"ub_table-of-contents\" data-showtext=\"show\" data-hidetext=\"hide\" data-scrolltype=\"auto\" id=\"ub_table-of-contents-80626d96-aacf-4287-ba2c-2d7fadb3abca\" data-initiallyhideonmobile=\"false\"\n                    data-initiallyshow=\"true\"><div class=\"ub_table-of-contents-extra-container\"><div class=\"ub_table-of-contents-container ub_table-of-contents-1-column \"><ul><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/unit-circle#0-what-is-a-unit-circle-in-math>What is a Unit Circle in Math?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/unit-circle#2-equation-of-a-unit-circle>Equation of a Unit Circle<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/unit-circle#3-finding-trigonometric-functions-using-a-unit-circle>Finding Trigonometric Functions Using a Unit Circle<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/unit-circle#11-solved-examples-on-unit-circle->Solved Examples on Unit Circle<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/unit-circle#12-practice-problems-on-unit-circle>Practice Problems on Unit Circle<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/unit-circle#13-frequently-asked-questions-on-unit-circle>Frequently Asked Questions on Unit Circle<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"0-what-is-a-unit-circle-in-math\">What is a Unit Circle in Math?<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">A unit circle is a circle of unit radius with center at origin. A circle is a closed geometric figure such that all the points on its boundary are at equal distance from its center. For a unit circle, this distance is 1 unit, or the radius is 1 unit.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Let us learn the equation of the unit circle, and understand the ways to represent each of the points on the circumference of the unit circle, with the help of T-ratios.<\/p>\n\n\n\n<div id=\"recommended-games-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Games<\/h4><div class=\"recommended-games-container-slides\"><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-multiples-of-100-in-unit-form\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/add_sub_pv_add_multiples_100_pt.png\" alt=\"Add Multiples of 100 in Unit Form Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add Multiples of 100 in Unit Form Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/area-with-unit-squares-and-side-lengths\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geo_meas_area_unit_sq_side_length_pt.png\" alt=\"Area with Unit Squares and Side Lengths Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Area with Unit Squares and Side Lengths Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/choose-the-correct-unit-of-capacity\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/measurement_estimate_capacity_2_pt.png\" alt=\"Choose the Correct Unit of Capacity Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Choose the Correct Unit of Capacity Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/compare-the-units-of-length\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/measurement_comp_metric_length_pt.png\" alt=\"Compare the Units of Length Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Compare the Units of Length Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/compare-unit-fractions-on-the-number-line\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/fractions_compare_unit_fraction_nl_pt.png\" alt=\"Compare Unit Fractions on the Number Line Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Compare Unit Fractions on the Number Line Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/compare-unit-fractions-using-real-world-models\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/fractions_compare_real_model_unit_pt.png\" alt=\"Compare Unit Fractions using Real World Models Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Compare Unit Fractions using Real World Models Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/compare-unit-fractions-using-visual-models\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/fractions_compare_strips_unit_pt.png\" alt=\"Compare Unit Fractions using Visual Models Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Compare Unit Fractions using Visual Models Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/compare-unit-fractions-without-visual-models\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/fractions_compare_without_visual_pt.png\" alt=\"Compare Unit Fractions without Visual Models Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Compare Unit Fractions without Visual Models Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/complete-the-unit-form\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/place_value_write_expanded_3d_pt.png\" alt=\"Complete the Unit Form Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Complete the Unit Form Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/conversion-tables-for-customary-units-of-capacity\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/measurement_conv_table_capacity_customary_pt.png\" alt=\"Conversion Tables for Customary Units of Capacity Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Conversion Tables for Customary Units of Capacity Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/games\">More Games<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-games-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".game-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            function adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    container.style.maxWidth = \"30%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    container.style.textAlign = \"center\";\n                } else {\n                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            }\n\n            function checkScrollPosition() {\n                const maxScrollLeft = slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading eplus-wrapper\" id=\"1-unit-circle-definition\">Unit Circle: Definition<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">The unit circle is a circle with a radius of one unit.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The unit circle is fundamentally related to the concepts of trigonometry. The trigonometric functions can be defined using the unit circle.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">A unit circle on the Cartesian plane is shown below. It has its center at origin and all the points on the circumference are at a distance of 1 unit from the center.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"356\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/unit-circle.png\" alt=\"Unit circle\" class=\"wp-image-32594\" title=\"Unit circle\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/unit-circle.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/unit-circle-300x172.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<div id=\"recommended-worksheets-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Worksheets<\/h4><div class=\"recommended-games-container-slides\"><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/circle-equivalent-fractions\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/circle-equivalent-fractions.jpeg\" alt=\"Circle Equivalent Fractions Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/count-rods-unit-blocks\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/count-rods-unit-blocks.jpeg\" alt=\"Count Rods & Unit Blocks Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/create-area-models-to-multiply-unit-fractions\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/create-area-models-to-multiply-unit-fractions.jpeg\" alt=\"Create Area Models to Multiply Unit Fractions Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/draw-area-models-to-multiply-unit-fractions\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/draw-area-models-to-multiply-unit-fractions.jpeg\" alt=\"Draw Area Models to Multiply Unit Fractions Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/express-fractions-as-sum-of-unit-fractions\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/express-fractions-as-sum-of-unit-fractions.jpeg\" alt=\"Express Fractions as Sum of Unit Fractions Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/fraction-multiplication-as-sum-of-unit-fractions\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/fraction-multiplication-as-sum-of-unit-fractions.jpeg\" alt=\"Fraction Multiplication as Sum of Unit Fractions Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/identify-the-place-value-units\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/identify-the-place-value-units.jpeg\" alt=\"Identify the Place Value Units Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/identify-the-unit-of-measurement\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/identify-the-unit-of-measurement.jpeg\" alt=\"Identify the Unit of Measurement Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/multiplying-non-unit-fractions\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/multiplying-non-unit-fractions.jpeg\" alt=\"Multiplying Non Unit Fractions Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/multiplying-unit-fractions\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/multiplying-unit-fractions.jpeg\" alt=\"Multiplying Unit Fractions Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/worksheets\">More Worksheets<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-worksheets-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".worksheet-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            function adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    container.style.maxWidth = \"30%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    container.style.textAlign = \"center\";\n                } else {\n                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            }\n\n            function checkScrollPosition() {\n                const maxScrollLeft = slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading eplus-wrapper\" id=\"2-equation-of-a-unit-circle\">Equation of a Unit Circle<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">The general equation of a circle is of the form $(x \\;-\\; a)^2 + (y \\;-\\; b)^2 = r^2$, where the center of the circle is (a, b) and the radius is r. A unit circle in the x-y plane is formed with a center at origin (0,0) and radius 1.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Thus, the equation $(x \\;-\\; a)^2 + (y \\;-\\; b)^2 = r^2$ becomes<\/p>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;$(x \\;-\\; 0)^2 + (y \\;-\\; 0)^2 = 1^2$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$&nbsp;x^2 + y^2 = 1$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Thus, the equation of the unit circle on an x-y plane is $x^2 + y^2 = 1$.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"3-finding-trigonometric-functions-using-a-unit-circle\">Finding Trigonometric Functions Using a Unit Circle<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">We can find trigonometric ratios using the unit circle. Consider the right triangle constructed in the unit circle shown in the diagram below.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Let P(x,y) be any point on the circle such that the line joining the origin and the point P makes angle with the positive x-axis. The radius of the circle (length = 1 unit) represents the hypotenuse of the right triangle. So, the sides of the right triangle are 1, x, y.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"308\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/trigonometric-functions-using-a-unit-circle.png\" alt=\"Trigonometric functions using a unit circle\" class=\"wp-image-32596\" title=\"Trigonometric functions using a unit circle\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/trigonometric-functions-using-a-unit-circle.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/trigonometric-functions-using-a-unit-circle-300x149.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">By the definition of the trigonometric ratios, we have<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$sin\\; \\theta = \\frac{Opposite\\; Side}{Hypotenuse} = \\frac{y}{1}$ &nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\Rightarrow y = sin\\theta$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$cos\\; \\theta = \\frac{Adjacent\\; Side}{Hypotenuse} = \\frac{x}{1}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\Rightarrow x = cos\\theta$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Thus, $P(x,y) = P(cos\\theta ,\\; sin\\theta )$<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"423\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/coordinates-of-a-point-on-a-unit-circle.png\" alt=\"Coordinates of a point on a unit circle\" class=\"wp-image-32597\" title=\"Coordinates of a point on a unit circle\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/coordinates-of-a-point-on-a-unit-circle.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/coordinates-of-a-point-on-a-unit-circle-300x205.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"4-unit-circle-with-sin-cos-and-tan\">Unit Circle with Sin, Cos, and Tan<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">We just learnt that coordinates of any point on the unit circle are equal to $(cos\\; \\theta,\\; sin\\; \\theta )$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Thus, $x = cos\\; \\theta$ and $y = sin\\; \\theta$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Using these values, we can further calculate $tan\\; \\theta = \\frac{sin\\; \\theta}{cos\\; \\theta}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Example:<\/strong> Find the value of tan $60^\\circ$ using sin and cos values from the unit circle.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">We know that, tan$ \\;60^{\\circ} = \\frac{sin\\; 60^\\circ}{cos\\; 60^\\circ}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Refer to the unit circle chart. We get the values<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$sin\\; 60^\\circ = \\frac{1}{2}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$cos\\; 60^\\circ = \\frac{\\sqrt{3}}{2}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Therefore, tan $60^\\circ = \\frac{1}{2}\\frac{\\sqrt{3}}{2}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">tan $60^\\circ = \\frac{1}{3}$<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"5-unit-circle-and-trigonometric-values\">Unit Circle and Trigonometric Values<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">The unit circle can be used to find all the trigonometric values. Let\u2019s see some examples.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">When $\\theta = 0^\\circ$, we have $x = 1$ and $y = 0$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Thus,<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$x = cos\\; \\theta = cos\\; 0^\\circ = 1$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">and&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$y = sin\\; \\theta = sin\\; 0^ \\circ = 0$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Similarly, for $= 45^\\circ$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$x = cos\\; 45^\\circ = \\frac{1}{\\sqrt{2}}$ and $y = sin\\; 45^\\circ = \\frac{1}{\\sqrt{2}}$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">If a right triangle is placed in a unit circle in the cartesian coordinate plane, with hypotenuse, base, and altitude measuring 1, x, y units respectively, then the unit circle identities can be given as,<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">$sin\\;(\\theta) = y$<\/li>\n\n\n\n<li class=\"eplus-wrapper\">$cos\\;(\\theta) = x$<\/li>\n\n\n\n<li class=\"eplus-wrapper\">$tan\\;(\\\\theta) = \\frac{sin\\; \\theta}{cos\\; \\theta} = \\frac{y}{x}$<\/li>\n\n\n\n<li class=\"eplus-wrapper\">$sec\\;(\\theta) = \\frac{1}{x}$<\/li>\n\n\n\n<li class=\"eplus-wrapper\">$cosec\\;(\\theta) = \\frac{1}{y}$<\/li>\n\n\n\n<li class=\"eplus-wrapper\">$cot\\;(\\theta = \\frac{cos\\; \\theta}{sin\\; \\theta} = \\frac{x}{y}$<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper\">In the next section, we will look at the <strong>unit circle with radians <\/strong>and <strong>unit circle degrees<\/strong>.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"6-unit-circle-and-pythagorean-identities\">Unit Circle and Pythagorean Identities<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">Let us observe how we derive these <strong>unit circle equations<\/strong> considering a unit circle.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">A point on the unit circle can be represented by the coordinates $cos\\; \\theta$ and $sin\\; \\theta$ .<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Here, $x = cos\\; \\theta,\\; $y = sin\\; \\theta$.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"395\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/unit-circle-1.png\" alt=\"Unit circle\" class=\"wp-image-32598\" title=\"Unit circle\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/unit-circle-1.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/unit-circle-1-300x191.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">The sides of the right triangle in the unit circle have the values of $sin\\; \\theta$ and $cos\\; \\theta$.<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper\">Applying the Pythagorean theorem, we can write $x^2 + y^2 = 1$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Substitute x and y, we get-<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$sin^2\\; \\theta + cos^2 \\;\\theta = 1$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">This equation is known as Pythagorean Identity.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">It is true for all the values of $\\theta$ in the unit circle.<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Using this first Pythagorean Identity, we can find the rest of the Pythagorean Identities.<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper\">$sin^2\\; \\theta + cos^2\\; \\theta = 1$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Dividing each term by $cos^2 \\theta$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\frac{sin^2\\;\\theta}{cos^2\\;\\theta} + \\frac{cos^2\\;\\theta}{cos^2\\;\\theta} = \\frac{1}{cos^2\\;\\theta}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$tan^2\\; \\theta + 1 = sec^2\\;\\theta$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">This is the second Pythagorean Identity.<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Now, on dividing each term of first equation by $sin^2\\; \\theta$, we get<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper\">$\\frac{sin^2\\; \\theta}{sin^2\\;\\theta} + \\frac{cos^2\\;\\theta}{sin^2\\;\\theta} = \\frac{1}{sin^2\\;\\theta}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$1 + cot^2\\; \\theta = cosec^2\\theta$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">This is the third Pythagorean Identity.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"7-unit-circle-chart-in-radians-and-degrees\">Unit Circle Chart in Radians and Degrees<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">The unit circle chart in radians is given in the diagram below. It represents a total angle of 2 radians or 360.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"621\" height=\"447\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/unit-circle-chart-in-radians.png\" alt=\"Unit circle chart in radians\" class=\"wp-image-32599\" title=\"Unit circle chart in radians\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/unit-circle-chart-in-radians.png 621w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/unit-circle-chart-in-radians-300x216.png 300w\" sizes=\"auto, (max-width: 621px) 100vw, 621px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">The unit circle is divided into four quadrants by the intersection of x-axis and y-axis. The points which represent the angles $\\frac{\\pi}{0},\\; \\frac{\\pi}{6},\\; \\frac{\\pi}{4},\\; \\frac{\\pi}{3},\\; \\frac{\\pi}{2}$ are the standard values of the trigonometric cosine and sine ratios.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The diagram shows unit circle values in both radians and degrees.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"606\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/unit-circle-chart-in-radians-and-degrees.png\" alt=\"Unit circle chart in radians and degrees\" class=\"wp-image-32600\" title=\"Unit circle chart in radians and degrees\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/unit-circle-chart-in-radians-and-degrees.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/unit-circle-chart-in-radians-and-degrees-300x293.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"8-unit-circle-and-trigonometric-values\">Unit Circle and Trigonometric Values<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">The unit circle can be used to find the various trigonometric identities and their principal angle values. Let\u2019s see some examples.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"344\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/unit-circle-and-trigonometric-values.png\" alt=\"Unit circle and trigonometric values\" class=\"wp-image-32601\" title=\"Unit circle and trigonometric values\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/unit-circle-and-trigonometric-values.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/unit-circle-and-trigonometric-values-300x166.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">When $= \\theta\\; 0^\\circ$, we have $x = 1$ and $y = 0$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$x = cos\\; \\theta = cos\\; 0^\\circ = 1$&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$y = sin\\; \\theta = sin\\; 0^\\circ = 0$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Similarly, for $\\theta = 45^\\circ$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$x = cos 45^\\circ = \\frac{1}{\\sqrt{2}}$ and $y = sin\\; 45^ = \\frac{1}{\\sqrt{2}}$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Let us now look at another angle of $90^\\circ$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Here, the value of cos $90^\\circ = 1$, and sin $90^\\circ = 1$.&nbsp;<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"9-unit-circle-table\">Unit Circle Table<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">The unit circle table helps to list the coordinates of the points on the unit circle and corresponding common angles using trigonometric ratios.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"468\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/unit-circle-table-of-trigonometric-ratios-and-values.png\" alt=\"Unit circle table of trigonometric ratios and values\" class=\"wp-image-32602\" title=\"Unit circle table of trigonometric ratios and values\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/unit-circle-table-of-trigonometric-ratios-and-values.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/unit-circle-table-of-trigonometric-ratios-and-values-300x226.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">The table above can be used as a unit circle calculator. We can find the rest of the ratios, namely secant, cosecant, and cotangent functions using the given formulas:<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$sec\\; \\theta&nbsp; = \\frac{1}{cos\\; \\theta}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$cosec\\; \\theta = \\frac{1}{sin\\; \\theta}$ &nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$cot\\; \\theta&nbsp; = \\frac{1}{sin\\; \\theta}$<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"10-conclusion\">Conclusion<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">In this article, we discussed unit circle and its properties. We saw some properties of trigonometry. And along with the concept of trigonometry, we solved T-ratios. We studied the unit circle chart. We solved many problems related to it.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"11-solved-examples-on-unit-circle-\">Solved Examples on Unit Circle<br><\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><strong>1. Does the point A <\/strong>$( \\frac{1}{4},\\; \\frac{1}{4})$<strong> lie on the unit circle?<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">We know that equation of a unit circle is:<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$x^2 + y^2 = 1$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Substituting $x = \\frac{1}{4}$&nbsp; and $y = \\frac{1}{4}$ , we get:<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$= x^2 + y^2$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$= \\frac{1^2}{4} + \\frac{1^2}{4}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$= \\frac{1}{16} + \\frac{1}{16}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$= \\frac{2}{16}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$= \\frac{1}{8}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\neq 1$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Since, $x^2 + y^2 \\neq 1$ , the point A $(\\frac{1}{4},\\;\\frac{1}{4})$ does not lie on the unit circle.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>2. Does the point A <\/strong>$(\\frac{1}{8},\\; \\frac{1}{8})$<strong> lie on the unit circle?<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">We know that equation of a unit circle is:<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$x^2 + y^2 = 1$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Substituting $x = \\frac{1}{8}$&nbsp; and $y = \\frac{1}{8}$ , we get:<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$= x^2 + y^2$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$= \\frac{1^2}{8} + \\frac{1^2}{8}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$= \\frac{1}{64} + \\frac{1}{64}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$= \\frac{2}{64}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$= \\frac{1}{32}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\neq 1$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;Since, $x^2 + y^2 \\neq 1$ , the point <strong>A <\/strong>$(\\frac{1}{8},\\; \\frac{1}{8})$ does not lie on the unit circle.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>3. If <\/strong>$sin\\; \\theta + cos\\; \\theta = \\frac{2}{3}$, <strong>what is <\/strong>$sin\\; \\theta.\\; cos\\; \\theta$<strong>?<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">Given $(sin\\; \\theta + cos\\; \\theta) = \\frac{2}{3}$<strong> <\/strong>&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Squaring both sides,<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$(sin\\; \\theta + cos\\; \\theta)^2 = (\\frac{2}{3})^2$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$sin^2\\;\\theta + cos^2\\; \\theta + 2\\; sin\\; \\theta\\; cos \\theta = \\frac{4}{9}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$1 + 2\\; sin\\; \\theta\\; cos\\; \\theta = \\frac{4}{9}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$2\\; sin\\; \\theta\\; cos\\; \\theta  = (\\frac{4}{9}) \\;-\\; 1 = \\frac{- 5}{9}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$sin\\; \\theta\\; cos\\; \\theta = \\frac{-5}{18}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>4.&nbsp; If <\/strong>$sin\\; \\theta = \\frac{4}{5}$<strong>, find the value of <\/strong>$cos\\; \\theta$<strong>.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">Here, we use the identity $sin^2\\; \\theta + cos^2\\; \\theta  = 1$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$(\\frac{4}{5})^2 + cos^2\\; \\theta = 1$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$cos\\; \\theta  = \\sqrt{1\\;-\\; (\\frac{4}{5})^2} = \\sqrt{\\frac{9}{25} = \\frac{3}{5}}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>5. What is the area of a unit circle?<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">The unit circle has radius $= 1$ unit.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$Area = \\pi r^2$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$Area = \\pi\\; square\\; units$<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"12-practice-problems-on-unit-circle\">Practice Problems on Unit Circle<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">Unit Circle - Definition, Chart, Equation, Examples, Facts<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">What is the Equation of a Unit Circle?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$x^2 + y^2 = 1$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$x^3 + y^3 = 1$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$x^3 + y^2 = 1$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$x^2 + y^3 = 1$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $x^2 + y^2 = 1$<br\/>The equation of a unit circle is $x^2 + y^2 = 1$.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">What is the value of cos $180^\\circ$ using the unit circle chart?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$0$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$-1$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$0.5$<\/div><div class=\"spq_answer_block\" data-value=\"3\">undefined<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $-1$<br\/>From the unit circle chart, we know that:<br>\r\n$x = -1$ and $y = 0$.<br>\r\nThus, $x = cos\\; 180^\\circ = -1$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">The radius of the unit circle is __________.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">0<\/div><div class=\"spq_answer_block\" data-value=\"1\">1<\/div><div class=\"spq_answer_block\" data-value=\"2\">0.5<\/div><div class=\"spq_answer_block\" data-value=\"3\">undefined<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 1<br\/>The unit circle has radius 1 unit.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">What is the value of tan $270^\\circ$ using the unit circle?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">0<\/div><div class=\"spq_answer_block\" data-value=\"1\">1<\/div><div class=\"spq_answer_block\" data-value=\"2\">0.5<\/div><div class=\"spq_answer_block\" data-value=\"3\">undefined<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: undefined<br\/>We know that<br>\r\n$tan\\; 270^\\circ = \\frac{sin\\; 270^\\circ}{cos\\; 270^\\circ}$<br>\r\nUsing the unit circle chart:<br>\r\n$sin\\; 270^\\circ = -1$<br>\r\n$cos\\; 210^\\circ = 0$<br>\r\nTherefore, $tan\\; 270^\\circ = -10 =$ undefined<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">5<\/span><h3 class=\"sqp_question_text\">Does the point A $(2 , 2)$ lie on the unit circle?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">Yes<\/div><div class=\"spq_answer_block\" data-value=\"1\">No<\/div><div class=\"spq_answer_block\" data-value=\"2\">Can't say<\/div><div class=\"spq_answer_block\" data-value=\"3\">Could be<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: No<br\/>We know that equation of a unit circle is:<br>\r\n$x^2 + y^2 = 1$<br>\r\nSubstituting $x = 2$  and $y = 2$, we get:<br>\r\n$= x^2 + y^2$<br>\r\n$= 2^2 + 2^2$<br>\r\n$= 4 + 4$<br>\r\n$= 8$<br>\r\n$\\neq 1$<br>\r\nSince, $x^2 + y^2 \\neq 1$, the point A $(2, 2)$ does not lie on the unit circle.<\/span><\/div><\/div><\/div><\/div>  <script type=\"application\/ld+json\">{\n        \"@context\": \"https:\/\/schema.org\/\", \n        \"@type\": \"Quiz\", \n        \"typicalAgeRange\": \"3-11\",\n        \"educationalLevel\":  \"beginner\",\n        \"assesses\" : \"Attend this quiz & Test your knowledge.\",\n        \"educationalAlignment\": [\n              {\n                \"@type\": \"AlignmentObject\",\n                \"alignmentType\": \"educationalSubject\",\n                \"targetName\": \"Math\"\n              }] ,\n        \"name\": \"Unit Circle - Definition, Chart, Equation, Examples, Facts\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Unit Circle\"\n        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\"Comment\",\n                                    \"text\": \"The equation of a unit circle is $$x^2 + y^2 = 1$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$x^3 + y^2 = 1$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The equation of a unit circle is $$x^2 + y^2 = 1$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$x^2 + y^3 = 1$$\",\n                                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\"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What is the value of cos $$180^\\\\circ$$ using the unit circle chart?\",\n                    \"text\": \"What is the value of cos $$180^\\\\circ$$ using the unit circle chart?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"From the unit circle chart, we know that:<br>\r\n$$x = -1$$ and $$y = 0$$.<br>\r\nThus, $$x = cos\\\\; 180^\\\\circ = -1$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$0$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"From the unit circle chart, we know that:<br>\r\n$$x = -1$$ and $$y = 0$$.<br>\r\nThus, $$x = cos\\\\; 180^\\\\circ = -1$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$0.5$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"From the unit circle chart, we know that:<br>\r\n$$x = -1$$ and $$y = 0$$.<br>\r\nThus, $$x = cos\\\\; 180^\\\\circ = -1$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"undefined\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"From the unit circle chart, we know that:<br>\r\n$$x = -1$$ and $$y = 0$$.<br>\r\nThus, $$x = cos\\\\; 180^\\\\circ = -1$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$-1$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"From the unit circle chart, we know that:<br>\r\n$$x = -1$$ and $$y = 0$$.<br>\r\nThus, $$x = cos\\\\; 180^\\\\circ = -1$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"From the unit circle chart, we know that:<br>\r\n$$x = -1$$ and $$y = 0$$.<br>\r\nThus, $$x = cos\\\\; 180^\\\\circ = -1$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The radius of the unit circle is __________.\",\n                    \"text\": \"The radius of the unit circle is __________.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The unit circle has radius 1 unit.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"0\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The unit circle has radius 1 unit.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"0.5\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The unit circle has radius 1 unit.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"undefined\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The unit circle has radius 1 unit.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"1\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The unit circle has radius 1 unit.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The unit circle has radius 1 unit.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What is the value of tan $$270^\\\\circ$$ using the unit circle?\",\n                    \"text\": \"What is the value of tan $$270^\\\\circ$$ using the unit circle?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"We know that<br>\r\n$$tan\\\\; 270^\\\\circ = \\\\frac{sin\\\\; 270^\\\\circ}{cos\\\\; 270^\\\\circ}$$<br>\r\nUsing the unit circle chart:<br>\r\n$$sin\\\\; 270^\\\\circ = -1$$<br>\r\n$$cos\\\\; 210^\\\\circ = 0$$<br>\r\nTherefore, $$tan\\\\; 270^\\\\circ = -10 =$$ undefined\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"0\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"We know that<br>\r\n$$tan\\\\; 270^\\\\circ = \\\\frac{sin\\\\; 270^\\\\circ}{cos\\\\; 270^\\\\circ}$$<br>\r\nUsing the unit circle chart:<br>\r\n$$sin\\\\; 270^\\\\circ = -1$$<br>\r\n$$cos\\\\; 210^\\\\circ = 0$$<br>\r\nTherefore, $$tan\\\\; 270^\\\\circ = -10 =$$ undefined\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"1\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"We know that<br>\r\n$$tan\\\\; 270^\\\\circ = \\\\frac{sin\\\\; 270^\\\\circ}{cos\\\\; 270^\\\\circ}$$<br>\r\nUsing the unit circle chart:<br>\r\n$$sin\\\\; 270^\\\\circ = -1$$<br>\r\n$$cos\\\\; 210^\\\\circ = 0$$<br>\r\nTherefore, $$tan\\\\; 270^\\\\circ = -10 =$$ undefined\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"0.5\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"We know that<br>\r\n$$tan\\\\; 270^\\\\circ = \\\\frac{sin\\\\; 270^\\\\circ}{cos\\\\; 270^\\\\circ}$$<br>\r\nUsing the unit circle chart:<br>\r\n$$sin\\\\; 270^\\\\circ = -1$$<br>\r\n$$cos\\\\; 210^\\\\circ = 0$$<br>\r\nTherefore, $$tan\\\\; 270^\\\\circ = -10 =$$ undefined\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"undefined\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"We know that<br>\r\n$$tan\\\\; 270^\\\\circ = \\\\frac{sin\\\\; 270^\\\\circ}{cos\\\\; 270^\\\\circ}$$<br>\r\nUsing the unit circle chart:<br>\r\n$$sin\\\\; 270^\\\\circ = -1$$<br>\r\n$$cos\\\\; 210^\\\\circ = 0$$<br>\r\nTherefore, $$tan\\\\; 270^\\\\circ = -10 =$$ undefined\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"We know that<br>\r\n$$tan\\\\; 270^\\\\circ = \\\\frac{sin\\\\; 270^\\\\circ}{cos\\\\; 270^\\\\circ}$$<br>\r\nUsing the unit circle chart:<br>\r\n$$sin\\\\; 270^\\\\circ = -1$$<br>\r\n$$cos\\\\; 210^\\\\circ = 0$$<br>\r\nTherefore, $$tan\\\\; 270^\\\\circ = -10 =$$ undefined\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Does the point A $$(2 , 2)$$ lie on the unit circle?\",\n                    \"text\": \"Does the point A $$(2 , 2)$$ lie on the unit circle?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"We know that equation of a unit circle is:<br>\r\n$$x^2 + y^2 = 1$$<br>\r\nSubstituting $$x = 2$$  and $$y = 2$$, we get:<br>\r\n$$= x^2 + y^2$$<br>\r\n$$= 2^2 + 2^2$$<br>\r\n$$= 4 + 4$$<br>\r\n$$= 8$$<br>\r\n$$\\\\neq 1$$<br>\r\nSince, $$x^2 + y^2 \\\\neq 1$$, the point A $$(2, 2)$$ does not lie on the unit circle.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Yes\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"We know that equation of a unit circle is:<br>\r\n$$x^2 + y^2 = 1$$<br>\r\nSubstituting $$x = 2$$  and $$y = 2$$, we get:<br>\r\n$$= x^2 + y^2$$<br>\r\n$$= 2^2 + 2^2$$<br>\r\n$$= 4 + 4$$<br>\r\n$$= 8$$<br>\r\n$$\\\\neq 1$$<br>\r\nSince, $$x^2 + y^2 \\\\neq 1$$, the point A $$(2, 2)$$ does not lie on the unit circle.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Can't say\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"We know that equation of a unit circle is:<br>\r\n$$x^2 + y^2 = 1$$<br>\r\nSubstituting $$x = 2$$  and $$y = 2$$, we get:<br>\r\n$$= x^2 + y^2$$<br>\r\n$$= 2^2 + 2^2$$<br>\r\n$$= 4 + 4$$<br>\r\n$$= 8$$<br>\r\n$$\\\\neq 1$$<br>\r\nSince, $$x^2 + y^2 \\\\neq 1$$, the point A $$(2, 2)$$ does not lie on the unit circle.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Could be\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"We know that equation of a unit circle is:<br>\r\n$$x^2 + y^2 = 1$$<br>\r\nSubstituting $$x = 2$$  and $$y = 2$$, we get:<br>\r\n$$= x^2 + y^2$$<br>\r\n$$= 2^2 + 2^2$$<br>\r\n$$= 4 + 4$$<br>\r\n$$= 8$$<br>\r\n$$\\\\neq 1$$<br>\r\nSince, $$x^2 + y^2 \\\\neq 1$$, the point A $$(2, 2)$$ does not lie on the unit circle.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"No\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"We know that equation of a unit circle is:<br>\r\n$$x^2 + y^2 = 1$$<br>\r\nSubstituting $$x = 2$$  and $$y = 2$$, we get:<br>\r\n$$= x^2 + y^2$$<br>\r\n$$= 2^2 + 2^2$$<br>\r\n$$= 4 + 4$$<br>\r\n$$= 8$$<br>\r\n$$\\\\neq 1$$<br>\r\nSince, $$x^2 + y^2 \\\\neq 1$$, the point A $$(2, 2)$$ does not lie on the unit circle.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"We know that equation of a unit circle is:<br>\r\n$$x^2 + y^2 = 1$$<br>\r\nSubstituting $$x = 2$$  and $$y = 2$$, we get:<br>\r\n$$= x^2 + y^2$$<br>\r\n$$= 2^2 + 2^2$$<br>\r\n$$= 4 + 4$$<br>\r\n$$= 8$$<br>\r\n$$\\\\neq 1$$<br>\r\nSince, $$x^2 + y^2 \\\\neq 1$$, the point A $$(2, 2)$$ does not lie on the unit circle.\"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"13-frequently-asked-questions-on-unit-circle\">Frequently Asked Questions on Unit Circle<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-5caa35dc-4ed6-4af4-b541-b3cb956da213\" data-mobilecollapse=\"true\" data-desktopcollapse=\"true\">\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-0-5caa35dc-4ed6-4af4-b541-b3cb956da213\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-5caa35dc-4ed6-4af4-b541-b3cb956da213\"><strong>What is the tangent of a circle?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-0-5caa35dc-4ed6-4af4-b541-b3cb956da213\">\n\n<p class=\"eplus-wrapper\">A line that touches the circle at one point is called a tangent to the circle.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The intersecting point at which the tangent touches the circle is known as its point of contact.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"276\" height=\"245\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/03\/unit-circle-Practice-Problems.png\" alt=\"Tangent of a circle\" class=\"wp-image-26874\"\/><\/figure>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-1-5caa35dc-4ed6-4af4-b541-b3cb956da213\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-5caa35dc-4ed6-4af4-b541-b3cb956da213\"><strong>What are the applications of trigonometry?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-1-5caa35dc-4ed6-4af4-b541-b3cb956da213\">\n\n<p class=\"eplus-wrapper\">Trigonometry is used in various fields like astronomy, oceanography, electronics, navigation, etc.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-2-5caa35dc-4ed6-4af4-b541-b3cb956da213\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-5caa35dc-4ed6-4af4-b541-b3cb956da213\"><strong>What is the radius of a unit circle?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-2-5caa35dc-4ed6-4af4-b541-b3cb956da213\">\n\n<p class=\"eplus-wrapper\">The radius of a unit circle is 1 unit.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-3-5caa35dc-4ed6-4af4-b541-b3cb956da213\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-5caa35dc-4ed6-4af4-b541-b3cb956da213\"><strong>What is the unit circle with tangent?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-3-5caa35dc-4ed6-4af4-b541-b3cb956da213\">\n\n<p class=\"eplus-wrapper\">The unit circle gives the values of sine and cosine function. However, the unit circle with tangent gives the values of the tangent function or tan function for different angles between 0 and 360 degrees.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What is a Unit Circle in Math? A unit circle is a circle of unit radius with center at origin. A circle is a closed geometric figure such that all the points on its boundary are at equal distance from its center. For a unit circle, this distance is 1 unit, or the radius is &#8230; <a title=\"Unit Circle &#8211; Definition, Chart, Equation, Examples, Facts\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/unit-circle\" aria-label=\"More on Unit Circle &#8211; Definition, Chart, Equation, Examples, Facts\">Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ub_ctt_via":"","footnotes":""},"categories":[1],"tags":[],"class_list":["post-26870","post","type-post","status-publish","format-standard","hentry","category-all"],"featured_image_src":null,"author_info":{"display_name":"Mithun Jhawar","author_link":"https:\/\/www.splashlearn.com\/math-vocabulary\/author\/mithun-jhawarsplashlearn-com\/"},"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/26870","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/comments?post=26870"}],"version-history":[{"count":12,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/26870\/revisions"}],"predecessor-version":[{"id":37703,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/26870\/revisions\/37703"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=26870"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=26870"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=26870"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}