6. Trigonometric Identities and More Equations

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

cos² (π/6) - sin² (π/6)

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

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

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

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

Simplify each expression. See Example 4.

cos² 2x - sin² 2x

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

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

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

sin 9x - sin 3x

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

sin 102° - sin 95°

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

2 cos 85° sin 140°

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

2x, given tan x = 5/3 and sin x < 0

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.

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

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

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

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: $\cos 2\theta$

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