Chapter 5.1, Problem 42E

To determine

To identify: All angles that are coterminal with $-{305}^{\circ }$ . Then find one positive angle and one negative angle that are coterminal with $-{305}^{\circ }$ .

Answer to Problem 42E

  ${55}^{\circ }\text{ positive coterminal, }-{665}^{\circ }\text{ negative coterminal}$

Explanation of Solution

Given information: $-{305}^{\circ }$

Calculation:

  $\theta =-{305}^{\circ }$

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 ${55}^{\circ }$ coterminal angle.

If we subtract ${360}^{\circ }\text{s}\left(k=1\right)$ we get $-{665}^{\circ }\text{s}$ for a negative coterminal angle.

  ${55}^{\circ }\text{ positive coterminal, }-{665}^{\circ }\text{ negative coterminal}$