Chapter 12.1, Problem 60WE

To determine

Find a first-quadrant angle $\theta ,0°<\theta <90°$ ,for which an angle six times as large as $\theta$ will be in the given quadrant.

Answer to Problem 60WE

  $\theta =50°$

Explanation of Solution

Given:

Fourth quadrant

Calculation:

Given $6\theta$ is in fourth quadrant.

So,

  $\begin{array}{l}270°<6\theta <360°\\ \Rightarrow \frac{270°}{6}<\frac{6\theta }{6}<\frac{360°}{6}\mathrm{...............}[\text{divide by 6]}\\ \Rightarrow 45°<\theta <60°\end{array}$

So, let $\theta =50°$

Check $6\theta =300°$ is in fourth quadrant.

So, the solution is $\theta =50°$ .