Chapter 4.1, Problem 38E

a.

To determine

To Convert : The radian measure to degree measure of angle $-\frac{7\pi }{12}$ .

Answer to Problem 38E

  $-\frac{7\pi }{12}=-{105}^{°}$

Explanation of Solution

Given information:

The radian measure of angle is $-\frac{7\pi }{12}$

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 $-\frac{7\pi }{12}$

To convert the radian measure to degree multiply the radian measure by $\begin{array}{l}\frac{{180}^{°}}{\pi }\\ -\frac{7\pi }{12}=-\frac{7\pi }{12}rad\times \left(\frac{{180}^{°}}{\pi rad}\right)\\ -\frac{7\pi }{12}=-{105}^{°}\end{array}$

Conclusion:

  $-\frac{7\pi }{12}=-{105}^{°}$

b.

To determine

To Convert : The radian measure to degree measure of angle $\frac{5\pi }{4}$ .

Answer to Problem 38E

  $\frac{5\pi }{4}={225}^{°}$

Explanation of Solution

Given information:

The radian measure of angle is $\frac{5\pi }{4}$

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 $\frac{5\pi }{4}$

To convert the radian measure to degree multiply the radian measure by $\begin{array}{l}\frac{{180}^{°}}{\pi }\\ \frac{5\pi }{4}=\frac{5\pi }{4}rad\times \left(\frac{{180}^{°}}{\pi rad}\right)\\ \frac{5\pi }{4}={225}^{°}\end{array}$

Conclusion:

  $\frac{5\pi }{4}={225}^{°}$