6. Trigonometric Identities and More Equations

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

sin 60° cos 45° - cos 60° sin 45°

In Exercises 57–64, find the exact value of the following under the given conditions:

a. cos (α + β)

sin α = 3/5, α lies in quadrant I, and sin β = 5/13, β lies in quadrant II.

Use the identities for the cosine of a sum or difference to write each expression as a trigonometric function of θ alone.

cos(90° + θ)

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

c. tan(α + β)

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

Use the given information to find sin(s + t). See Example 3.

cos s = -1/5 and sin t = 3/5, s and t in quadrant II

Use the identities for the cosine of a sum or difference to write each expression as a trigonometric function of θ alone.

cos(270° + θ)

Find one value of θ or x that satisfies each of the following.

sin θ = cos(2θ + 30°)

Use the identities for the cosine of a sum or difference to write each expression as a trigonometric function of θ alone.

cos(90° - θ)

Use the given information to find sin(s + t). See Example 3.

cos s = -15/17 and sin t = 4/5, s in quadrant II and t in quadrant I

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

a. sin(α + β)

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

Verify that each equation is an identity (Hint: cos 2x = cos(x + x).)

cos( π/2 + x) = -sin x

In Exercises 35–38, find the exact value of the following under the given conditions: b. cos(α﹣β)

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

Expand the expression using the sum & difference identities and simplify.

$\(\tan\[\left\)(-\(\theta\)-\(\frac{\pi}{2}\]\right\))$

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

a. sin(α + β)

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

Express each function as a trigonometric function of x. See Example 5.

cos 3x