6. Trigonometric Identities and More Equations

Use the given information to find the quadrant of s + t. See Example 3.

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

Use the formula for the cosine of the difference of two angles to solve Exercises 1–12. In Exercises 1–4, find the exact value of each expression. cos(45° - 30°)

Each expression is the right side of the formula for cos (α - β) with particular values for α and β. Write the expression as the cosine of an angle.

$\cos \frac{5\pi }{12}\cos \frac{\pi }{12}+\sin \frac{5\pi }{12}\sin \frac{\pi }{12}$

Each expression is the right side of the formula for cos (α - β) with particular values for α and β. Find the exact value of the expression.

$\cos \frac{5\pi }{12}\cos \frac{\pi }{12}+\sin \frac{5\pi }{12}\sin \frac{\pi }{12}$

Use one or more of the six sum and difference identities to solve Exercises 13–54. In Exercises 13–24, find the exact value of each expression. cos(135° + 30°)

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.

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

a. cos (α + β)

tan α = ﹣3/4, α lies in quadrant II, and cos β = 1/3, β lies in quadrant I.

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

a. cos (α + β)

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

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

a. cos (α + β)

tan α = 3/4, 𝝅 < α < 3𝝅/2, and cos β = 1/4, 3𝝅/2 < β < 2𝝅

In Exercises 69–74, rewrite each expression as a simplified expression containing one term. cos (α + β) cos β + sin (α + β) sin β