Chapter 9.4, Problem 5GP

Solution

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

  $\theta ={293.6}^{\circ }$ .

Given:

  $\cos \theta =0.4;{270}^{\circ }<\theta <{360}^{\circ }$

Calculation:

By using the calculator, the angle whose cosine is 0.4 is,

  $\begin{array}{c}\theta ={\cos }^{-1}\left(0.4\right)\\ \approx {66.4}^{\circ }\end{array}$

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

  $\begin{array}{c}\theta \approx {360}^{\circ }-{66.4}^{\circ }\\ ={293.6}^{\circ }\end{array}$