Chapter 14.4, Problem 1CYP

To determine

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

Answer to Problem 1CYP

  $\frac{-4\sqrt{2}}{9}$

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:

  $\sin 2\theta =2\sin \theta \cos \theta$

Calculation:

  

  $\begin{array}{l}\cos \theta =-\frac{1}{3}\\ \sin \theta =\frac{2\sqrt{2}}{3}\\ \sin 2\theta =2\sin \theta \cos \theta \\ \sin 2\theta =2\times \left(\frac{2\sqrt{2}}{3}\right)\times \left(\frac{-1}{3}\right)=\frac{-4\sqrt{2}}{9}\end{array}$