Chapter 5.1, Problem 16CFU

To determine

To find: The measure of the reference angle for $-{210}^{\circ }$ .

Answer to Problem 16CFU

  ${30}^{\circ }\text{s}$

Explanation of Solution

Given information: $-{210}^{\circ }$

Calculation:

  $-{210}^{\circ }$

This is the angle.

We want the reference angle which is the angle the terminal side makes the x -axis.

First let’s find a coterminal angle with a measure between 0 and 360 degrees.

  $-{210}^{\circ }+{360}^{\circ }={150}^{\circ }\text{s}$

The reference angle for a coterminal angles is the same.

This angle is in quadrant II.

So we subtract it from ${180}^{\circ }\text{s}$ .

  ${180}^{\circ }-{150}^{\circ }={30}^{\circ }\text{s}$

  ${30}^{\circ }\text{s}$