Use identities to find the indicated value for each angle measure.
-$\cos 2 \theta = - \frac { 5 } { 7 }$ and $\frac { \pi } { 2 }

Question

Use identities to find the indicated value for each angle measure.
-$\cos 2 \theta = - \frac { 5 } { 7 }$ and $\frac { \pi } { 2 } < \theta < \pi \quad$ Find $\sin \theta$

Quizplus · Accepted Answer

Using the double-angle identity for cosine, we have:$$\cos 2\theta = 1 - 2\sin^2 \theta$$Substituting the given value of $\cos 2\theta$, we get:$$-\frac{5}{7} = 1 - 2\sin^2 \theta$$Solving for $\sin^2 \theta$, we get:$$\sin^2 \theta = \frac{6}{7}$$Taking the square root of both sides, we get:$$\sin \theta = \pm \frac{\sqrt{42}}{7}$$Since $\frac{\pi}{2} < \theta < \pi$, $\sin \theta$ is positive. Therefore,$$\sin \theta = \frac{\sqrt{42}}{7}$$

Use Identities to Find the Indicated Value for Each Angle cos⁡2θ=−57\cos 2 \theta = - \frac { 5 } { 7 }cos2θ=−75​

Use Identities to Find the Indicated Value for Each Angle $\cos 2 \theta = - \frac { 5 } { 7 }$