6. Trigonometric Identities and More Equations

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

sin 2π/3 = _____ (- π/6)

Find the exact value of each expression. See Example 1.

[tan 5π/12 + tan π/4]/[1 - tan 5π/12 tan π/4]

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

____ 72° = cot 18°

Write each function as an expression involving functions of θ or x alone. See Example 2.

cos(θ - 30°)

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

tan 24° = 1/ _____ 66°

Write each function as an expression involving functions of θ or x alone. See Example 2.

cos(45° - θ)

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

tan θ = cot(45° + 2θ)

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

sin θ = cos(2θ + 30°)

Write each function as an expression involving functions of θ or x alone. See Example 2.

sin(45° + θ)

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

sec x = csc (2π/3)

Write each function as an expression involving functions of θ or x alone. See Example 2.

tan (π/4 + x)

Write each function as an expression involving functions of θ or x alone. See Example 2.

sin (3π/4 - x)

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 as an expression involving functions of θ or x alone. See Example 2.

tan(180° + θ)

Write each function as an expression involving functions of θ or x alone. See Example 2.

sin(π + x)