Chapter 4, Problem 52RE

To determine

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

Answer to Problem 52RE

Reference angle $\theta \text{'}={85}^{\circ }$

Explanation of Solution

Given information:

Consider $\theta ={635}^0$

Calculation:

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

  $\theta ={635}^0={360}^0+{275}^0$

  ${275}^0$ is in fourth quadrant

Reference angle

  $\begin{array}{l}\theta \text{'}=360-\theta \\ =360-275\\ ={85}^{\circ }\end{array}$

Graph of the standard angle and reference angle.

Hence, $\theta \text{'}={85}^{\circ }$ .