Chapter 12.4, Problem 40WE

To determine

Find the measure of two angles $\left(\theta \right)$ between $0°\text{ and }360°$ for the function $\sin \theta =-0.8300$ to the nearest tenth of a degree.

Answer to Problem 40WE

The two angles $\left(\theta \right)$ are $236.1°\text{ and }303.9°$ .

Explanation of Solution

Given information: The given function is $\sin \theta =-0.8300$ .

Calculation: The value of angle $\left(\theta \right)$ for the given function $\sin \theta =-0.8300$ is evaluated as,

  $\begin{array}{c}\sin \theta =-0.8300\mathrm{....}\left(\text{Given}\right)\\ \theta ={\sin }^{-1}\left(-0.8300\right)\\ =-56.1°\\ =-56.1°+\left(360°\right)\mathrm{....}\left(\begin{array}{l}\text{Add }360°\text{two }\\ \text{make it positive}\end{array}\right)\\ =303.9°\end{array}$

Now according to question $\sin \theta$ is negative and the angle $\left(\theta \right)$ obtained is $303.9°$ which is positive and can be written as $\left(303.9°=270°+33.9°\right)$ which lies in fourth quadrant therefore another angle can be obtained by subtracting $33.9°$ from $270°$ .

  $\begin{array}{c}\text{Second angle}=270°-33.9°\\ =236.1°\end{array}$