Chapter 4, Problem 54RE

To determine

To find: the reference angle $\theta \text{'}$ for the given angle $\theta .$

Answer to Problem 54RE

Reference angle $\theta \text{'}={60}^o$

Explanation of Solution

Given information:

Consider $\theta =\frac{17\pi }{3}$

Calculation:

Reference angle is the smallest angle between the x -axis and terminal side of the angle.

  $\theta =\frac{17\pi }{3}={1020}^o$

  ${1020}^0$ is in fourth quadrant

Reference angle

  $\begin{array}{l}\theta \text{'}=1080-1020\\ ={60}^o\end{array}$

Graph of the standard angle and reference angle.

Hence, $\theta \text{'}={60}^o$ .