Chapter 12.3, Problem 63WE

To determine

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

Answer to Problem 63WE

  $\theta ={15}^{\circ },{195}^{\circ }$

Explanation of Solution

Given information :

  $\tan \theta =\tan {15}^{\circ }$

  $\begin{array}{l}\tan \theta =\tan {15}^{\circ }\\ \theta ={\tan }^{-1}\left(\tan {15}^{\circ }\right)\end{array}$

We know that the value of tan is positive inI and III quadrant.

Hence the values here can be fromI and III quadrant.

We may write $\tan {15}^{\circ }=\tan \left({180}^{\circ }+{15}^{\circ }\right)=\tan {195}^{\circ }$

Hence the values in the given range are,

  $\theta ={15}^{\circ },{195}^{\circ }$