Use identities to find the indicated value for each angle measure.
-$\cos 2 \theta = - \frac { 7 } { 9 }$ and $\frac { \pi } { 2 }

Question

Use identities to find the indicated value for each angle measure.
-$\cos 2 \theta = - \frac { 7 } { 9 }$ and $\frac { \pi } { 2 } < \theta < \pi \quad$ Find $\sin \theta$.
A) $\sin \theta = \frac { 2 \sqrt { 2 } } { 3 }$
B) $\sin \theta = - \frac { 2 \sqrt { 2 } } { 3 }$
C) $\sin \theta = \frac { 3 \sqrt { 2 } } { 4 }$
D) $\sin \theta = 0$

Quizplus · Accepted Answer

Using the identity $\cos 2 \theta = 1 - 2 \sin^2 \theta$, we have$$1 - 2 \sin^2 \theta = - \frac { 7 } { 9 }$$$$2 \sin^2 \theta = 1 + \frac { 7 } { 9 } = \frac { 16 } { 9 }$$$$\sin^2 \theta = \frac { 8 } { 9 }$$$$\sin \theta = \pm \frac { 2 \sqrt { 2 } } { 3 }$$Since $\frac { \pi } { 2 } < \theta < \pi$, $\sin \theta$ is positive. Therefore, $\sin \theta = \frac { 2 \sqrt { 2 } } { 3 }$.

Use Identities to Find the Indicated Value for Each Angle cos⁡2θ=−79\cos 2 \theta = - \frac { 7 } { 9 }cos2θ=−97​

Use Identities to Find the Indicated Value for Each Angle $\cos 2 \theta = - \frac { 7 } { 9 }$