Chapter 12.3, Problem 61WE

To determine

To find all angles $\theta ,0^{\circ }\le \theta <{360}^{\circ }$ , that makes the given statement true.

Answer to Problem 61WE

  $\theta ={150}^{\circ },{210}^{\circ }$

Explanation of Solution

Given information :

  $\cos \theta =-\frac{\sqrt{3}}{2}$

  $\begin{array}{l}\cos \theta =-\frac{\sqrt{3}}{2}\\ \theta ={\cos }^{-1}\left(-\frac{\sqrt{3}}{2}\right)\end{array}$

We know that the value of cosine is negative in II and III quadrant.

Hence the values here can be from II and III quadrant.

Hence the values in the given range are,

  $\theta ={150}^{\circ },{210}^{\circ }$