Chapter 13.4, Problem 2AGP

To determine

To Find: The value of $\cos 2\theta$

Answer to Problem 2AGP

  $\frac{-7}{9}$

Explanation of Solution

Given Information:

We know that, the given expression is the value of $\cos \theta =-\frac{1}{3},{90}^{\circ }<\theta <{180}^{\circ }$

Formula used:

  $\cos 2\theta =2{\cos }^2\theta -1$

Calculation:

  $\begin{array}{l}\cos 2\theta =2{\cos }^2\theta -1\\ \because \cos \theta =\frac{-1}{3}\\ \cos 2\theta =2\times {\left(\frac{-1}{3}\right)}^2-1\\ \cos 2\theta =\frac{2}{9}-1\\ \cos 2\theta =\frac{-7}{9}\end{array}$