Chapter 12.4, Problem 45WE

To determine

Find the measure of angle $\left(\theta \right)$ to the nearest tenth of degree between $0°\text{ and }360°$ for the function $\sin \theta =-0.6118$ and satisfy the condition $\cos \theta >0$ .

Answer to Problem 45WE

The angle $\left(\theta \right)$ is equal to $322.3°$ .

Explanation of Solution

Given information: The given function is $\sin \theta =-0.6118$ which satisfy the condition $\cos \theta >0$ .

Calculation: The value of angle $\left(\theta \right)$ for the given function $\sin \theta =-0.6118$ is evaluated as,

  $\begin{array}{c}\sin \theta =-0.6118\mathrm{....}\left(\text{Given}\right)\\ \theta ={\sin }^{-1}\left(-0.6118\right)\\ =-37.7°\\ =-37.7°+\left(360°\right)\mathrm{....}\left(\begin{array}{l}\text{Add 360}°\text{ to }\\ \text{make positive}\end{array}\right)\\ =322.3°\text{ for }\cos \theta >0\end{array}$