Chapter 12.4, Problem 46WE

To determine

Find the measure of angle $\left(\theta \right)$ to the nearest tenth of degree between $0°\text{ and }360°$ for the function $\cos \theta =0.7815$ and satisfy the condition $\tan \theta <0$ .

Answer to Problem 46WE

The angle $\left(\theta \right)$ is equal to $321.4°$ .

Explanation of Solution

Given information: The given function is $\cos \theta =0.7815$ which satisfy the condition $\tan \theta <0$ .

Calculation: The value of angle $\left(\theta \right)$ for the given function $\cos \theta =0.7815$ is evaluated as,

  $\begin{array}{c}\cos \theta =0.7815\mathrm{....}\left(\text{Given}\right)\\ \theta ={\cos }^{-1}\left(0.7815\right)\\ =38.6°\\ =\left(360°\right)-38.6°\mathrm{....}\left(\begin{array}{l}\text{Subtract 38}\text{.6}°\text{ form 360}°\\ \text{for the condition tan}\theta <0\end{array}\right)\\ =321.4°\text{ for }\tan \theta <0\end{array}$