6. Trigonometric Identities and More Equations

Verify that each equation is an identity.

sin(x + y) + sin(x - y) = 2 sin x cos y

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

sin(45° + θ)

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

c. tan (α + β)

cos α = 8/17, α lies in quadrant IV, and sin β = -1/2, β lies in quadrant III.

Use the given information to cos(x - y).

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

Find the exact value of each expression.

tan (5π/12)

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

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

Find the exact value of each expression.

tan 285°

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

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

Find the exact value of each expression.

sin (-13π/12)

Find the exact value of each expression. (Do not use a calculator.)

cos (-7π/12)

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

sin 98.0142°

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

cos(45° - θ)

Use the result from Exercise 80 to find the acute angle between each pair of lines. (Note that the tangent of the angle will be positive.) Use a calculator, and round to the nearest tenth of a degree.

x + y = 9, 2x + y = -1

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

c. tan (α + β)

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