Chapter 9.2, Problem 22E

To determine

To find: The positive and the negative angle that is conterminal with the given angle.

Answer to Problem 22E

The positive conterminal angle is $\frac{15\pi }{4}$ and negative is $-\frac{\pi }{4}$ .

Explanation of Solution

Given:

The given diagram is shown in Figure 1

  

Figure 1

Calculation:

Consider the given degree measure is $315°$ .

Consider the conversion of the degree measure to the radian measure is,

  $\begin{array}{c}315°=315°\left(\frac{\pi }{180°}\right)\\ =\frac{7\pi }{4}\text{radians}\end{array}$

Consider the formula to determine the positive conterminal angle is,

  $\theta =\theta +2\pi$

Then,

  $\begin{array}{c}\frac{7\pi }{4}=\frac{7\pi }{4}+2\pi \\ =\frac{15\pi }{4}\end{array}$

Consider the formula to determine the negative conterminal angle is,

  $\theta =\theta -2\pi$

Then,

  $\begin{array}{c}\frac{7\pi }{4}=\frac{7\pi }{4}-2\pi \\ =-\frac{\pi }{4}\end{array}$

Thus, the positive conterminal angle is $\frac{15\pi }{4}$ and negative is $-\frac{\pi }{4}$ .