Chapter 4.1, Problem 29E

(a)

To determine

To calculate:coterminal angles for ${120}^{\circ }$

Answer to Problem 29E

  $-{240}^{\circ },{480}^{\circ }$

Explanation of Solution

Given information: angle is ${120}^{\circ }$

Formula used:For angle $\theta$ , coterminal angles are given by $\theta +360°$ and $\theta -360°$ .

Calculation:

Take $\theta =120°$

Coterminal angles are given by $\theta +360°$ and $\theta -360°$

So,

Coterminal angles are calculated as follows:

  $\begin{array}{l}\theta +360°={120}^{\circ }+{360}^{\circ }={480}^{\circ }\\ \theta -120°={120}^{\circ }-{360}^{\circ }=-{240}^{\circ }\end{array}$

(b)

To determine

To find:coterminal angles of $-210°$

Answer to Problem 29E

  $150°,-480°$

Explanation of Solution

Given information:Angle is $-210°$

Formula used: For angle $\theta$ , coterminal angles are given by $\theta +360°$ and $\theta -360°$ .

Calculation:

Take $\theta =-210°$

Coterminal angles are given by $\theta +360°$ and $\theta -360°$

So,

Coterminal angles are calculated as follows:

  $\begin{array}{l}\theta +360°=-{210}^{\circ }+{360}^{\circ }={150}^{\circ }\\ \theta -120°=-{210}^{\circ }-{360}^{\circ }=-{480}^{\circ }\end{array}$