Use identities to find the indicated value for each angle measure.
-$\cos 2 \theta = \frac { 2 } { 3 }$ and $\theta$ terminates in quadrant III Find $\cos \theta$.
A) $\cos \theta = - \frac { \sqrt { 30 } } { 5 }$
B) $\cos \theta = - \frac { \sqrt { 30 } } { 6 }$
C) $\cos \theta = 0$
D) $\cos \theta = \frac { \sqrt { 30 } } { 6 }$

Question

Quizplus · Accepted Answer

In quadrant III, cosine is negative. Using the identity $\cos 2\theta = 2\cos^2\theta - 1$, solve for $\cos \theta$: $\frac{2}{3} = 2\cos^2\theta - 1$. Solving gives $\cos \theta = \pm \frac{\sqrt{30}}{6}$. Since $\theta$ is in quadrant III, $\cos \theta$ is negative, so $\cos \theta = -\frac{\sqrt{30}}{6}$.

Use Identities to Find the Indicated Value for Each Angle cos⁡2θ=23\cos 2 \theta = \frac { 2 } { 3 }cos2θ=32​

Use Identities to Find the Indicated Value for Each Angle $\cos 2 \theta = \frac { 2 } { 3 }$