Chapter 5, Problem 38SGA

To determine

To identify: All angles that are coterminal with $-{45}^{\circ }$ . Then find one positive angle and one negative angle that are coterminal with $-{45}^{\circ }$ .

Answer to Problem 38SGA

  ${315}^{\circ }\text{ positive coterminal, }-{405}^{\circ }\text{ negative coterminal}$

Explanation of Solution

Given information: $-{45}^{\circ }$

Calculation:

  $\theta =-{45}^{\circ }$

The expression for a group of angles, all coterminal with an angle would be

  $\text{coterminal angle = }{\theta }^{\circ }+{360}^{\circ }k\text{ where }k\text{ is an integer}$

For our angle if we add ${360}^{\circ }\text{s}\left(k=1\right)$ we get positive ${315}^{\circ }$ coterminal angle.

If we subtract ${360}^{\circ }\text{s}\left(k=1\right)$ we get $-{405}^{\circ }\text{s}$ for a negative coterminal angle.

  ${315}^{\circ }\text{ positive coterminal, }-{405}^{\circ }\text{ negative coterminal}$