Chapter 12.3, Problem 65WE

To determine

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

Answer to Problem 65WE

  $\theta ={70}^{\circ },{290}^{\circ }$

Explanation of Solution

Given information :

  $\cos \theta =\cos {70}^{\circ }$

  $\begin{array}{l}\cos \theta =\cos {70}^{\circ }\\ \theta ={\cos }^{-1}\left(\cos {70}^{\circ }\right)\end{array}$

We know that the value of cosine is positive inI and IVquadrant.

Hence the values here can be fromI and IVquadrant.

Therefore we can also write $\cos {70}^{\circ }=\cos \left({360}^{\circ }-{70}^{\circ }\right)=\cos {290}^{\circ }$

Hence the values in the given range are,

  $\theta ={70}^{\circ },\left({360}^{\circ }-{70}^{\circ }\right)={290}^{\circ }$