Chapter 9.4, Problem 7GP

Solution

To solve: the given equation for $\theta$ .

  $\theta ={346.7}^{\circ }$ .

Given:

  $\sin \theta =-0.23;{270}^{\circ }<\theta <{360}^{\circ }$

Calculation:

By using the calculator, the angle whose sine is $-0.23$ is,

  $\begin{array}{c}\theta ={\sin }^{-1}\left(-0.23\right)\\ \approx -{13.3}^{\circ }\end{array}$

Now the angle in the Quadrant IV $\left({270}^{\circ }<\theta <{360}^{\circ }\right)$ that has the same sine value is,

  $\begin{array}{c}\theta \approx {360}^{\circ }-{13.3}^{\circ }\\ ={346.7}^{\circ }\end{array}$