Chapter 12.4, Problem 42WE

To determine

Find the measure of two angles $\left(\theta \right)$ between $0°\text{ and }360°$ for the function $\tan \theta =0.6182$ to the nearest tenth of a degree.

Answer to Problem 42WE

The two angles $\left(\theta \right)$ are $31.7°\text{ and }211.7°$ .

Explanation of Solution

Given information: The given function is $\tan \theta =0.6182$ .

Calculation: The value of angle $\left(\theta \right)$ for the given function $\tan \theta =0.6182$ is evaluated as,

  $\begin{array}{c}\tan \theta =0.6182\mathrm{....}\left(\text{Given}\right)\\ \theta ={\tan }^{-1}\left(0.6182\right)\\ =31.7°\end{array}$

Now according to question $\tan \theta =0.6182$ is positive and the angle $\left(\theta \right)$ obtained is $31.7°$ which is also positive and lies in first quadrant, therefore another angle can be obtained by adding $31.7°$ in $180°$ .

  $\begin{array}{c}\text{Second angle}=31.7°+180°\\ =211.7°\end{array}$