6. Trigonometric Identities and More Equations

Determine whether each statement is true or false. If false, tell why. See Example 4. cos(30° + 60°) = cos 30° + cos 60°

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)

Write each function value in terms of the cofunction of a complementary angle.

sin (2π/5)

Write each function value in terms of the cofunction of a complementary angle.

sin 142° 14'

Write each function value in terms of the cofunction of a complementary angle.

cot (9π/10)

Write each function value in terms of the cofunction of a complementary angle.

tan 174° 03'

Write each function value in terms of the cofunction of a complementary angle.

sin 98.0142°

Use identities to fill in each blank with the appropriate trigonometric function name.

sin 2π/3 = _____ (- π/6)

Use identities to fill in each blank with the appropriate trigonometric function name.

____ 72° = cot 18°

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

cot(θ - 10°) = tan(2θ - 20°)

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.