Use identities to find the indicated value for each angle measure.
-$\cos 2 \theta = - \frac { 3 } { 8 }$ and $\frac { \pi } { 2 }

Question

Use identities to find the indicated value for each angle measure.
-$\cos 2 \theta = - \frac { 3 } { 8 }$ and $\frac { \pi } { 2 } < \theta < \pi \quad$ Find $\sin \theta$.
A) $\sin \theta = - \frac { \sqrt { 11 } } { 4 }$
B) $\sin \theta = \frac { \sqrt { 11 } } { 4 }$
C) $\sin \theta = 0$
D) $\sin \theta =$

Quizplus · Accepted Answer

Given $\cos 2\theta = -\frac{3}{8}$ and $\frac{\pi}{2} < \theta < \pi$, we use the double angle identity for cosine, $\cos 2\theta = 2\cos^2\theta - 1$, to find $\cos\theta$. Solving for $\cos\theta$ gives two possible values, but only one is in the correct quadrant (II, where cosine is negative and sine is positive). Then, using $\sin^2\theta + \cos^2\theta = 1$, we find $\sin\theta = \frac{\sqrt{11}}{4}$, considering the positive root due to the angle's quadrant.

Use Identities to Find the Indicated Value for Each Angle cos⁡2θ=−38\cos 2 \theta = - \frac { 3 } { 8 }cos2θ=−83​

Use Identities to Find the Indicated Value for Each Angle $\cos 2 \theta = - \frac { 3 } { 8 }$