Use identities to find the indicated value for each angle measure.
-$\sin \theta = - \frac { 4 } { 5 } , \frac { 3 \pi } { 2 }

Question

Use identities to find the indicated value for each angle measure.
-$\sin \theta = - \frac { 4 } { 5 } , \frac { 3 \pi } { 2 } < \theta < 2 \pi \quad$ Find $\cos ( 2 \theta )$
A) $- \frac { 7 } { 25 }$
B) $\frac { 24 } { 25 }$
C) $\frac { 7 } { 25 }$
D) $- \frac { 24 } { 25 }$

Quizplus · Accepted Answer

Given $\sin \theta = -\frac{4}{5}$ and $\frac{3\pi}{2} < \theta < 2\pi$, we are in the fourth quadrant where sine is negative and cosine is positive. To find $\cos(2\theta)$, we use the double angle formula: $\cos(2\theta) = 1 - 2\sin^2(\theta)$. Substituting $\sin(\theta) = -\frac{4}{5}$ gives $\cos(2\theta) = 1 - 2\left(-\frac{4}{5}\right)^2 = 1 - 2\left(\frac{16}{25}\right) = 1 - \frac{32}{25} = -\frac{7}{25}$.

Use Identities to Find the Indicated Value for Each Angle sin⁡θ=−45,3π2<θ<2π\sin \theta = - \frac { 4 } { 5 } , \frac { 3 \pi } { 2 } < \theta < 2 \pi \quadsinθ=−54​,23π​<θ<2π

Use Identities to Find the Indicated Value for Each Angle $\sin \theta = - \frac { 4 } { 5 } , \frac { 3 \pi } { 2 } < \theta < 2 \pi \quad$