6. Trigonometric Identities and More Equations

Solve each equation over the interval [0°, 360°). Write solutions as exact values or to the nearest tenth of a degree, as appropriate.

sin 2θ = cos 2θ +1

Simplify each expression. See Example 4.

cos² π/8 - 1/2

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.

Verify that each equation is an identity.

cos x = (1 - tan² (x/2))/(1 + tan² (x/2))

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

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

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

d. sin 2α

sin α = -1/3, 𝝅 < α < 3𝝅/2, and cos β = -1/3, 𝝅 < β < 3𝝅/2.

In Exercises 39–42, use double- and half-angle formulas to find the exact value of each expression. cos² 15° - sin² 15°

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

2θ, given cos θ = -12/13 and sin θ > 0

Simplify each expression. See Example 4.

2 tan 15°/(1 - tan² 15°)

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

cot θ = 2, θ lies in quadrant III.

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

(2 tan (π/3))/(1 - tan² (π/3))