Question

Rewrite each degree measure in radians and each radian measure in degrees if the angle is$120°$.

Short answer

The degree measure in radians of angle $120°$is $\frac{2\pi }{3}\text{rad}$.

Step-by-step solution

Step 1. Write down the given information.

The given angle in degrees measure is $120°$.

Step 2. Concept used.

From the degree – radian conversion rule.

$\pi \text{Radian}=180{}^{\circ }....\left(1\right)$

Step 3. Convert degrees measures to radians.

The angle $120°$in radian units is evaluated with the help of concept (1) stated above.

$\begin{array}{l}{120}^{°}={120}^{°}\times \frac{\pi }{{180}^{°}}\text{rad}\\ =\frac{2\pi }{3}\text{rad}\end{array}$

Step 4. Conclusion.

The degree measure in radians of angle $120°$is $\frac{2\pi }{3}\text{rad}$.