In Exercises 1–6, use the figures to find the exact value of each trigonometric function.
sin 2α

In Exercises 35–38, find the exact value of the following under the given conditions:

d. sin 2α

sin α = -1/3, 𝝅 < α < 3𝝅/2, and cos β = -1/3, 𝝅 < β < 3𝝅/2.

Given $\(\tan\]\theta\)=\(\frac{5}{12}\)$ and 0 < $\(\theta\)$ < $\(\frac{\pi}{2}\)$, find $\(\cos\[\left\)(2\(\theta\]\right\))$.

Find values of the sine and cosine functions for each angle measure.

2x, given tan x = 5/3 and sin x < 0

Find values of the sine and cosine functions for each angle measure.

2θ, given cos θ = (√3)/5 and sin θ > 0

Find values of the sine and cosine functions for each angle measure.

θ, given cos 2θ = 3/4 and θ terminates in quadrant III

Find values of the sine and cosine functions for each angle measure.

θ, given cos 2θ = 2/3 and 90° < θ <180°