Chapter 12.4, Problem 38WE

To determine

Find the measure of two angles $\left(\theta \right)$ between $0°\text{ and }360°$ for the function $\cos \theta =0.7851$ to the nearest tenth of a degree.

Answer to Problem 38WE

The two angles $\left(\theta \right)$ are $38.3°\text{ and }321.7°$ .

Explanation of Solution

Given information: The given function is $\cos \theta =0.7851$ .

Calculation: The value of angle $\left(\theta \right)$ for the given function $\cos \theta =0.7851$ is evaluated as,

  $\begin{array}{c}\cos \theta =0.7851\mathrm{....}\left(\text{Given}\right)\\ \theta ={\cos }^{-1}\left(0.7851\right)\\ =38.3°\end{array}$

Now according to question $\cos \theta$ is positive and the angle $\left(\theta \right)$ obtained is $38.3°$ which is positive, therefore another angle will lie in fourth quadrant because the first angle lies in first quadrant.

  $\begin{array}{c}\text{Second angle}=360-38.3\\ =321.7°\end{array}$