Use the information given about the angle $$\theta , 0 \leq \theta \leq 2 \pi$$ , to find the exact value of the indicated trigonometric function.
-$\sin \theta = - \frac { 4 } { 5 } , \frac { 3 \pi } { 2 }

Question

Use the information given about the angle $$\theta , 0 \leq \theta \leq 2 \pi$$ , to find the exact value of the indicated trigonometric function.
-$\sin \theta = - \frac { 4 } { 5 } , \frac { 3 \pi } { 2 } < \theta < 2 \pi \quad$ Find $\cos ( 2 \theta ) .$

A) $\frac { 24 } { 25 }$

B) $\frac { 7 } { 25 }$

C) $- \frac { 7 } { 25 }$

D) $- \frac { 24 } { 25 }$

Quizplus · Accepted Answer

In the given range, $\theta$ is in the fourth quadrant where cosine is positive. Using $\sin^2 \theta + \cos^2 \theta = 1$, we find $\cos \theta = \frac{3}{5}$. Then, $\cos(2\theta) = 2\cos^2\theta - 1 = 2(\frac{3}{5})^2 - 1 = \frac{18}{25} - 1 = -\frac{7}{25}$.

Use the Information Given About the Angle θ,0≤θ≤2π\theta , 0 \leq \theta \leq 2 \piθ,0≤θ≤2π

Use the Information Given About the Angle $\theta , 0 \leq \theta \leq 2 \pi$