Chapter 12.3, Problem 67WE

To determine

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

Answer to Problem 67WE

  $\theta ={20}^{\circ },{200}^{\circ }$

Explanation of Solution

Given information :

  $\tan \theta =\tan {20}^{\circ }$

  $\begin{array}{l}\tan \theta =\tan {20}^{\circ }\\ \theta ={\tan }^{-1}\left(\tan {20}^{\circ }\right)\end{array}$

Further we can write $\tan {20}^{\circ }=\tan \left({180}^{\circ }+{20}^{\circ }\right)=\tan {200}^{\circ }$

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

Hence the values here can be fromI and IIIquadrant.

Hence the values in the given range are,

  $\theta ={20}^{\circ },{200}^{\circ }$