Question

Rewrite each degree measure in radians and each radian measure in degrees if the angle is $-\frac{\pi }{6}$.

Short answer

The degree measure of angle $-\frac{\pi }{6}$is $-30°$.

Step-by-step solution

Step 1. Write down the given information.

The given angle in radian measure is$-\frac{\pi }{6}$.

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 $-\frac{\pi }{6}$in degrees units is evaluated with the help of concept (1) stated above.

$\begin{array}{l}-\frac{\pi }{6}=-\frac{1}{6}\left(\pi \right)\\ =-\frac{1}{6}\times \left({180}^{°}\right)\\ ={30}^{°}\end{array}$

Step 4. Conclusion.

The degree measure of angle $-\frac{\pi }{6}$ is $30°$.