Chapter 9, Problem 10CT

To determine

To convert the degree measure to radians find one positive angle and one negative angle that are coterminal with the given angle.

Answer to Problem 10CT

The $-{50}^{\circ }$ degree measure to radian is $-\frac{5\pi }{18}$ , ${310}^{\circ },-{410}^{\circ }$

Explanation of Solution

Given:

The given angle is $-{50}^{\circ }$ .

Calculation:

It is known that $\pi$ radian $={180}^{\circ }$

Therefore, $1$ degree $\frac{\pi }{180}$ radian.

So, $\begin{array}{l}-{50}^{\circ }=\frac{\pi }{180}\times -{50}^{\circ }\text{ radian}\\ -{50}^{\circ }=-\frac{5\pi }{18}\text{ radian}\end{array}$

The positive angle coterminal with the given angle is ${360}^{\circ }-{50}^{\circ }={310}^{\circ }$

The negative angle coterminal with the given angle is $-{50}^{\circ }-{360}^{\circ }=-{410}^{\circ }$ .