7. Non-Right Triangles

In Exercises 35–38, find the exact value of the following under the given conditions:b. cos(α﹣β)3 𝝅 12 𝝅 sin α = ------- , 0 < α < -------- , and sin β = --------- , --------- < β < 𝝅. 5 2 13 2

In Exercises 35–36, the three given points are the vertices of a triangle. Solve each triangle, rounding lengths of sides to the nearest tenth and angle measures to the nearest degree.A(0, 0), B(-3, 4), C(3, -1)

In Exercises 35–38, find the exact value of the following under the given conditions:βe. cos -------21 3𝝅 1 3𝝅 sin α =﹣ ------ , 𝝅 < α < ------- , and cos β =﹣------ , 𝝅 < β < ---------. 3 2 3 2

In Exercises 35–38, find the exact value of the following under the given conditions:b. cos(α﹣β)1 3𝝅 1 3𝝅 sin α =﹣ ------ , 𝝅 < α < ------- , and cos β =﹣------ , 𝝅 < β < ---------. 3 2 3 2

In Exercises 57–64, find the exact value of the following under the given conditions:a. cos (α + β)3 5sin α = ------ , α lies in quadrant I, and sin β = ------- , β lies in quadrant II.5 13

In Exercises 57–64, find the exact value of the following under the given conditions:a. cos (α + β)3 1tan α = ﹣ ------ , α lies in quadrant II, and cos β = ------- , β lies in quadrant I.4 3

In Exercises 57–64, find the exact value of the following under the given conditions:a. cos (α + β)8 1cos α = ------ , α lies in quadrant IV, and sin β = ﹣------- , β lies in quadrant III.17 2

In Exercises 57–64, find the exact value of the following under the given conditions:a. cos (α + β)3 3𝝅 1 3𝝅 tan α = ------ , 𝝅 < α < -------- , and cos β = ------- , ---------- < β < 2𝝅.4 2 4 2

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