6. Trigonometric Identities and More Equations

Use the given information to find each of the following.

sin x, given cos 2x = 2/3 , with π < x < 3π/2

Simplify each expression.

√[(1 + cos 76°)/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

Match each expression in Column I with its value in Column II.

10. cos 67.5°

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

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

Use a half-angle identity to find each exact value.

sin 195°

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

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

Use a half-angle identity to find each exact value.

cos 195°

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

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