Chapter 5, Problem 39SGA

To determine

To identify: All angles that are coterminal with ${113}^{\circ }$ . Then find one positive angle and one negative angle that are coterminal with ${113}^{\circ }$ .

Answer to Problem 39SGA

  ${473}^{\circ }\text{ positive coterminal, }-{247}^{\circ }\text{ negative coterminal}$

Explanation of Solution

Given information: ${113}^{\circ }$

Calculation:

  $\theta ={113}^{\circ }$

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 ${473}^{\circ }$ coterminal angle.

If we subtract ${360}^{\circ }\text{s}\left(k=1\right)$ we get $-{247}^{\circ }\text{s}$ for a negative coterminal angle.

  ${473}^{\circ }\text{ positive coterminal, }-{247}^{\circ }\text{ negative coterminal}$