Chapter 12.4, Problem 39WE

To determine

Find the measure of two angles $\left(\theta \right)$ between $0°\text{ and }360°$ for the function $\tan \theta =-1.752$ to the nearest tenth of a degree.

Answer to Problem 39WE

The two angles $\left(\theta \right)$ are $299.7°\text{ and }119.7°$ .

Explanation of Solution

Given information: The given function is $\tan \theta =-1.752$ .

Calculation: The value of angle $\left(\theta \right)$ for the given function $\tan \theta =-1.752$ is evaluated as,

  $\begin{array}{c}\tan \theta =-1.752\mathrm{....}\left(\text{Given}\right)\\ \theta ={\tan }^{-1}\left(-1.752\right)\\ =-63.3°\\ =-60.3°+\left(360°\right)\mathrm{....}\left(\begin{array}{l}\text{Add }360°\text{two }\\ \text{make it positive}\end{array}\right)\\ =299.7°\end{array}$

Now according to question $\tan \theta$ is negative and the angle $\left(\theta \right)$ obtained is $299.7°$ which is positive, therefore another angle can be obtained by subtracting $180°$ from $299.7°$ .

  $\begin{array}{c}\text{Second angle}=299.7°-180\\ =119.7°\end{array}$