Chapter 4.1, Problem 37E

a.

To determine

To Convert : The radian measure to degree measure of angle $\frac{3\pi }{2}$ .

Answer to Problem 37E

  $\frac{3\pi }{2}={270}^{°}$

Explanation of Solution

Given information:

The radian measure of angle is $\frac{3\pi }{2}$

Concept and Formula Used:

To convert the radian measure to degree multiply the radian measure by $\frac{{180}^{°}}{\pi }$

Calculation:

The measure of the angle is $\frac{3\pi }{2}$

To convert the radian measure to degree multiply the radian measure by $\begin{array}{l}\frac{{180}^{°}}{\pi }\\ \frac{3\pi }{2}=\frac{3\pi }{2}rad\times \left(\frac{{180}^{°}}{\pi rad}\right)\\ \frac{3\pi }{2}={270}^{°}\end{array}$

Conclusion:

  $\frac{3\pi }{2}={270}^{°}$

b.

To determine

To Convert : The radian measure to degree measure of angle $-\frac{7\pi }{6}$ .

Answer to Problem 37E

  $-\frac{7\pi }{6}={210}^{°}$

Explanation of Solution

Given information:

The radian measure of angle is $-\frac{7\pi }{6}$

Concept and Formula Used:

To convert the radian measure to degree multiply the radian measure by $\frac{{180}^{°}}{\pi }$

Calculation:

The measure of the angle is $-\frac{7\pi }{6}$

To convert the radian measure to degree multiply the radian measure by $\begin{array}{l}\frac{{180}^{°}}{\pi }\\ -\frac{7\pi }{6}=-\frac{7\pi }{6}rad\times \left(\frac{{180}^{°}}{\pi rad}\right)\\ -\frac{7\pi }{6}={210}^{°}\end{array}$

Conclusion:

  $-\frac{7\pi }{6}={210}^{°}$