Chapter 9, Problem 11CT

To determine

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

Answer to Problem 11CT

The $\frac{4\pi }{5}$ radian measure to degree is ${144}^{\circ }$ , ${504}^{\circ },-{216}^{\circ }$

Explanation of Solution

Given:

The given angle is $\frac{4\pi }{5}$ .

Calculation:

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

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

So, $\begin{array}{l}\frac{4\pi }{5}\text{ radian}=\frac{180}{\pi }\times {\frac{4\pi }{5}}^{\circ }\\ \frac{4\pi }{5}\text{ radian}={144}^{\circ }\end{array}$

The positive angle coterminal with the given angle is ${360}^{\circ }+{144}^{\circ }={504}^{\circ }$

The negative angle coterminal with the given angle is ${144}^{\circ }-{360}^{\circ }=-{216}^{\circ }$ .