Chapter 13.4, Problem 2BGP

To determine

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

Answer to Problem 2BGP

  $\frac{4\sqrt{2}}{7}$

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:

  $\tan 2\theta =\frac{2\tan \theta }{1-{\tan }^2\theta }$

Calculation:

  $\begin{array}{l}\cos \theta =\frac{-1}{3}\\ \tan \theta =-2\sqrt{2}\\ \tan 2\theta =\frac{2\tan \theta }{1-{\tan }^2\theta }=\frac{2\times -2\sqrt{2}}{1-{(-2\sqrt{2})}^2}\\ \tan 2\theta =\frac{-4\sqrt{2}}{-7}\\ \tan 2\theta =\frac{4\sqrt{2}}{7}\end{array}$