Chapter 5.1, Problem 40E

To determine

To identify: All angles that are coterminal with ${217}^{\circ }$ . Then find one positive angle and one negative angle that are coterminal with ${217}^{\circ }$ .

Answer to Problem 40E

  ${577}^{\circ }\text{ positive coterminal, }-{143}^{\circ }\text{ negative coterminal}$

Explanation of Solution

Given information: ${217}^{\circ }$

Calculation:

  $\theta ={217}^{\circ }$

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 ${577}^{\circ }$ coterminal angle.

If we subtract ${360}^{\circ }\text{s}\left(k=1\right)$ we get $-{143}^{\circ }\text{s}$ for a negative coterminal angle.

  ${577}^{\circ }\text{ positive coterminal, }-{143}^{\circ }\text{ negative coterminal}$