6. Trigonometric Identities and More Equations

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

$\sin \theta =\frac{12}{13},\theta \text{ lies in quadrant II.}$

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

$\sin \theta =\frac{12}{13},\theta \text{ lies in quadrant II.}$

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

$\sin \theta =\frac{12}{13},\theta \text{ lies in quadrant II.}$

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

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

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

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

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°