Question

How do you convert $60$ degrees to radiant?

Answer 1

Hint: Degrees and radians are two different units that are used for the measurement of the angles. The conversion of degrees to radians is considered while measuring the angles in Geometry. The measure of the angle is generally denoted by degrees, having the symbol °. An angle can be determined by two different kinds of units, which are, degrees and radians. You can convert one form of the representation of any mathematical angle to the other by using simple formulas.

Complete step by step solution:
To Convert Degrees to Radians we use the formula given below
Angle in radians = Angle in degrees $ \times \dfrac{\pi }{{180}}$
The value of $\pi = \dfrac{{22}}{7}$ or $3.14$
Here, the angel value is given $60^\circ $
After putting value in formula, we get,
Angle in radians = Angle in degrees $ \times \dfrac{\pi }{{180}}$
$ = 60 \times \dfrac{\pi }{{180}}$
Here, $\dfrac{{60}}{{180}} = \dfrac{1}{3}$
Therefor,
Angle in radians $ = \dfrac{\pi }{3}$
Hence, $60$ degrees is equal to $\dfrac{\pi }{3}$ in radian.

Note: This is a very simple method and you can easily convert degrees to radians with this simple procedure and there is one other method to solve this question, a full circle measures ${360^o}$, but it also measures $2\pi $radians. ${60^ \circ }$ Is $\dfrac{1}{6}$ of a full circle, so an angle of ${60^ \circ }$ would be equal to $\dfrac{1}{6}$ of $2\pi $ radians. $\dfrac{1}{6} \times 2\pi $ Radians = $\dfrac{\pi }{3}$ radians.