6. Trigonometric Identities and More Equations

Write each expression as the sine, cosine, or tangent of a double angle. Then find the exact value of the expression. 2cos² 𝝅/8﹣ 1

In Exercises 47–54, use the figures to find the exact value of each trigonometric function. 2sin(θ/2)cos(θ/2)

Simplify each expression. See Example 4.

1 - 2 sin² 22 ½°

Write each expression as a product of trigonometric functions. See Example 8.

cos 5x + cos 8x

Simplify each expression. See Example 4.

tan 34°/2(1 - tan² 34°)

Use the given information to find the exact value of each of the following: cos 2θ

cot θ = 2, θ lies in quadrant III.

Use the given information to find the exact value of each of the following: $\sin 2\theta$

$\cos \theta =\frac{24}{25},\theta \text{ lies in quadrant IV.}$

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

d. sin 2α

sin α = 3/5, 0 < α < 𝝅/2, and sin β = 12/13, 𝝅/2 < β < 𝝅.

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

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

Solve each equation (x in radians and θ in degrees) for all exact solutions where appropriate. Round approximate answers in radians to four decimal places and approximate answers in degrees to the nearest tenth. Write answers using the least possible nonnegative angle measures.

1 - sin x = cos 2x