6. Trigonometric Identities and More Equations

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

sin 5π/9 cos π/18 - cos 5π/9 sin π/18 .

Use the given information to find sin(x + y).

sin y = - 2/3 , cos x = - 1/5, x in quadrant II, y in quadrant III

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

sin 98.0142°

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

[tan 80° - tan(-55°)]/[ 1 + tan 80° tan(-55°)]

Use the given information to find sin(x + y).

cos x = 2/9, sin y = - 1, x in quadrant IV, y in quadrant III

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)