Chapter 7, Problem 31SGA

To determine

To find: the value of $\cos 2\theta$ by using given information.

Answer to Problem 31SGA

  $-\frac{7}{25}$

Explanation of Solution

Given information:

  $\cos \theta =\frac{3}{5},\text{ 0}°<\theta <90°$

Calculation:

Evaluate $\cos 2\theta$ by using the double angle identity of cosine as follows:

  $\begin{array}{c}\cos 2\theta =2{\cos }^2\theta -1\end{array}$

  $\begin{array}{c}=2{\left(\frac{3}{5}\right)}^2-1\left[\text{Put the value of cos}\theta \right]\end{array}$

  $\begin{array}{c}=\frac{18}{25}-1\end{array}$

  $\begin{array}{c}=-\frac{7}{25}\end{array}$

Thus the value of $\cos 2\theta$ is $-\frac{7}{25}$ .