Chapter 12.4, Problem 25OE

To determine

Explain how could you find the measures of two angles $\left(\theta \right)$ between $0°\text{ and }360°$ such that $\sin \left(\theta \right)=-0.5000$ .

Answer to Problem 25OE

The two angles $\left(\theta \right)$ will be $330°\text{ and }210°$ .

Explanation of Solution

Given information: The given function is $\sin \left(\theta \right)=-0.5000$ .

Calculation: In order to find the value of acute angle $\left(\theta \right)$ for the given function $\sin \left(\theta \right)=-0.5000$ , first evaluate the value of angle $\left(\theta \right)$ and then apply the given conditions. For example for the given function $\sin \left(\theta \right)=-0.5000$ the angle $\left(\theta \right)$ is evaluated as,

  $\begin{array}{c}\sin \left(\theta \right)=-0.5000\mathrm{....}\left(\text{Given}\right)\\ \theta ={\sin }^{-1}\left(-0.5000\right)\\ \theta =-30°\end{array}$

Now If we add $360°$ to angle $\theta =-30°$ then one angle can be obtained which will be $330°$ . And, if $330°$ is $60°$ more than $270°$ , therefore if we subtract $60°$ from $270°$ then the other angle can be obtained which will be $210°$ .