# 60 Degrees to Radians – Definition, Formula, Examples, Facts, FAQs

## What Is 60 Degrees to Radians Conversion?

60 degrees to radians is $\pi 3$

Degrees and radians are the units used to measure angles

Degree: A degree (denoted by °) is the amount of rotation from the initial arm to the terminal arm. A complete turn around the center of a circle is $360^{\circ}$. If it is divided into 360 equal parts, each part represents 1 degree.

Radian: An angle of 1 radian is defined to be the angle, in the counterclockwise direction, which spans an arc whose length is equal to the radius of the circle. Thus, if arc length $= r$, then angle is 1 radian. It holds true for all circles.

By the same logic, 2 radians is the central angle made by an arc whose length is $2 r$ (twice the length of the radius of the circle). If the arc-length equals the total circumference of the circle which is $2\pi r$, it represents an angle of $2\pi$ radians. Thus, a complete circle represents $2\pi$ radians

• $360^{\circ} = 2\pi$ radians
• $180^{\circ} = \pi$ radians
• $90^{\circ} = 2$ radians
• $60^{\circ} = 3$ radians
• $45^{\circ} = 4$ radians
• $30^{\circ} = 6$ radians

To convert an angle from degrees to radians, we multiply it by $180^{\circ}$.

Angle in degrees $\times \frac{\pi}{180^{\circ}} =$ Angle in radians

We can use this formula to convert 60 degrees to radians.

## How to Convert 60 Degrees into Radians

We use the conversion formula to convert 60 degrees into radians.

Angle in radians $=$ Angle in degrees $\times\frac{\pi}{180^{\circ}}$

Here, angle in degrees $= 60^{\circ}$

On substituting this in the formula, we get

Angle in radians $= 60^{\circ} \times \frac{\pi}{180^{\circ}} = \frac{\pi}{3}$

Thus, the value of 60 degrees to radians is 3.

Note:

We can also approach this problem in a different way. We know that the angle at the center of a circle is 360 degrees. It is equivalent to 2π in radians.

$360^{\circ} = 2\pi$

Dividing both sides by 6, we will get

$\frac{360^{\circ}}{6} = \frac{2\pi}{6}$

$60^{\circ} = \frac{\pi}{3}$

Thus, the value of 60 degrees to radians in terms of pi is $\frac{\pi}{3}$.

## Negative 60 Degrees to Radians

Negative angle is an angle generated in an clockwise direction from the initial arm. To convert a negative degree into a radian, we use the same method as we did for positive degrees. We will simply multiply the angle’s given value by $\frac{\pi}{180^{\circ}}$.

Let’s convert $-60^{\circ}$ into radians.

Radian $= (\frac{\pi}{180^{\circ}})$   (degrees)

Radian $= (\frac{\pi}{180^{\circ}}) \times (-60^{\circ})$

Angle in radian $= – \frac{\pi}{3}$

• $60^{\circ} = \frac{\pi}{3}; 30^{\circ} = \frac{\pi}{6}; 120^{\circ} = \frac{2\pi}{3}$
• $2\pi$ radians $= 360$ degrees.
• To convert radians to degrees, we multiply by $\frac{180^{\circ}}{\pi}$.
Angle in radians $\times \frac{180^{\circ}}{\pi} =$ Angle in degrees
• The symbol for radian given by “rad” or c is generally omitted in mathematical writing.

## Conclusion

In this article, we learned about the angle in radians equivalent to 60 degrees. We discussed the conversion formula along with some examples. Let’s solve a few more examples and practice problems for better understanding.

## Solved Examples on Degrees to Radians

1. Convert 60 degrees to radians.

Solution:

To convert $60^{\circ}$ to radians, use the formula

Angle in radians $=$ Angle in degrees $\times (\frac{\pi}{180^{\circ}})$

Therefore, $60^{\circ} \times (\frac{\pi}{180^{\circ}}) = (\frac{\pi}{3})$  radians

So, 60 degrees in radians is $(\frac{\pi}{3})$  radians.

2. Convert 90 degrees to radians.

Solution:

Given: 90 degrees is the angle

Angle in radian $=$ Angle in degree $\times (\frac{\pi}{180^{\circ}})$

Angle in radian $= 90^{\circ} \times (\frac{\pi}{180^{\circ}})$

Angle in radian $= \frac{\pi}{2}$

Hence, 90 degrees is equal to $\frac{\pi}{2}$ in radians.

3. Convert 49 radians to degrees.

Solution:

Angle in Degrees $=$ Angle in Radians $\times \frac{\pi}{180^{\circ}}$

Angle in Degrees $= (\frac{4\pi}{9}) \times \frac{\pi}{180^{\circ}}$

Angle in Degrees $= 4 \times 20^{\circ}$

Angle in Degrees $= 80^{\circ}$

Hence, $\frac{4\pi}{9}$  radians are 80 degrees.

4. Convert 200 degrees into radians.

Solution:

By the formula, we know

Angle in radians $=$ Angle in degree $\times \frac{\pi}{180^{\circ}}$

Thus, 200 degrees in radians  $= 200 \times \frac{\pi}{180^{\circ}} = \frac{10\pi}{9}$ radians.

Hence, 200 degrees is equal to $\frac{10\pi}{9}$ in radians.

## Practice Problems on Degrees to Radians

1

### Convert $\pi$ radian to degrees.

$180^{\circ}$
$57^{\circ}$
$54^{\circ}$
$360^{\circ}$
CorrectIncorrect
Correct answer is: $180^{\circ}$
Radians $\times(\frac{180^{\circ}}{\pi}) =$ Degrees
radians $= \times (\frac{180^{\circ}}{\pi}) = 180^{\circ}$
2

### Convert $30^{\circ}$ to radians.

$\frac{\pi}{6}$
$\frac{\pi}{9}$
$\frac{2 \pi}{3}$
$\frac{\pi}{4}$
CorrectIncorrect
Correct answer is: $\frac{\pi}{6}$
$30^{\circ} \times (\frac{\pi}{180^{\circ}}) = \frac{\pi}{6}$
3

### Convert $75^{\circ}$ to radians.

$\frac{\pi}{4}$
$\frac{5 \pi}{12}$
$\frac{3 \pi}{4}$
$\frac{2 \pi}{3}$
CorrectIncorrect
Correct answer is: $\frac{5 \pi}{12}$
Degrees $\times (\frac{\pi}{180^{\circ}}) =$ Radians
$75^{\circ} \times (\frac{\pi}{180^{\circ}}) = \frac{5 \pi}{12}$
4

### How many radians is 60 degrees?

$\frac{3\pi}{2}$
$\frac{\pi}{2}$
$\frac{\pi}{3}$
$\frac{\pi}{6}$
CorrectIncorrect
Correct answer is: $\frac{\pi}{3}$
60 degrees $= \frac{\pi}{3}$ radians
5

### If $60^{\circ} = \frac{\pi}{3}$, then $120^{\circ} =$ _____ .

$\frac{\pi}{6}$
$\frac{2 \pi}{3}$
$\frac{\pi}{2}$
$2\pi$
CorrectIncorrect
Correct answer is: $\frac{2 \pi}{3}$
$60^{\circ} = \frac{\pi}{3}$
$120^{\circ} = \frac{2\pi}{3}$

Radians and degrees are connected by the relationship $360^{\circ} = 2\pi$ radians.
• If you wish to convert from degrees to radians, multiply the given degree measure by $\frac{\pi}{180}$.
• If you wish to convert from radians to degrees, multiply the given radian measure by $\frac{\pi}{180}$.
240 degrees is $\frac{4\pi}{3} radians. 120 degrees is$\frac{2\pi}{3}\$ radians.