6. Trigonometric Identities and More Equations

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

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

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

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

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

cot θ = 2, θ lies in quadrant III.

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 2θ

cot θ = 2, θ lies in quadrant III.

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

sin θ = ﹣2/3, θ lies in quadrant III.

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

sin θ = ﹣2/3, θ lies in quadrant III.

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

sin θ = ﹣2/3, θ lies in quadrant III.

In Exercises 15–22, write each expression as the sine, cosine, or tangent of a double angle. Then find the exact value of the expression. 2 sin 15° cos 15°

Write each expression as the sine, cosine, or tangent of a double angle. Then find the exact value of the expression. cos² 105° - sin² 105°

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)

Write each expression as a sum or difference of trigonometric functions. See Example 7.

5 cos 3x cos 2x

Write each expression as a sum or difference of trigonometric functions. See Example 7.

8 sin 7x sin 9x