6. Trigonometric Identities and More Equations

Sum and Difference Identities

Open Question
In Exercises 35–38, find the exact value of the following under the given conditions:a. sin(α + β)3 𝝅 12 𝝅sin α = ------- , 0 < α < -------- , and sin β = --------- , --------- < β < 𝝅.5 2 13 2
Open Question
In Exercises 35–38, find the exact value of the following under the given conditions:a. sin(α + β) 1 3𝝅 1 3𝝅 sin α =﹣ ------ , 𝝅 < α < ------- , and cos β =﹣------ , 𝝅 < β < ---------. 3 2 3 2
Open Question
In Exercises 35–38, find the exact value of the following under the given conditions:c. tan(α + β) 1 3𝝅 1 3𝝅 sin α =﹣ ------ , 𝝅 < α < ------- , and cos β =﹣------ , 𝝅 < β < ---------. 3 2 3 2
Open Question
In Exercises 35–38, find the exact value of the following under the given conditions:d. sin 2α 1 3𝝅 1 3𝝅 sin α =﹣ ------ , 𝝅 < α < ------- , and cos β =﹣------ , 𝝅 < β < ---------. 3 2 3 2
Open Question
In Exercises 57–64, find the exact value of the following under the given conditions:c. tan (α + β)3 5sin α = ------ , α lies in quadrant I, and sin β = ------- , β lies in quadrant II.5 13
Open Question
In Exercises 57–64, find the exact value of the following under the given conditions:b. sin (α + β)3 5sin α = ------ , α lies in quadrant I, and sin β = ------- , β lies in quadrant II.5 13
Open Question
In Exercises 57–64, find the exact value of the following under the given conditions:c. tan (α + β)8 1cos α = ------ , α lies in quadrant IV, and sin β = ﹣------- , β lies in quadrant III.17 2
Open Question
In Exercises 57–64, find the exact value of the following under the given conditions:b. sin (α + β)8 1cos α = ------ , α lies in quadrant IV, and sin β = ﹣------- , β lies in quadrant III.17 2
Open Question
In Exercises 57–64, find the exact value of the following under the given conditions:c. tan (α + β)5 𝝅 3 3𝝅 sin α = ------ , -------- < α < 𝝅 , and tan β = ------- , 𝝅 < β < -------- .6 2 7 2
Open Question
In Exercises 57–64, find the exact value of the following under the given conditions:b. sin (α + β)5 𝝅 3 3𝝅 sin α = ------ , -------- < α < 𝝅 , and tan β = ------- , 𝝅 < β < -------- .6 2 7 2
Open Question
In Exercises 69–74, rewrite each expression as a simplified expression containing one term.sin (α - β) cos β + cos (α - β) sin β
Open Question
Use the given information to find cos(x - y).
sin y = - 2/3, cos x = -1/5, x in quadrant II, y in quadrant III
Open Question
Use the given information to find tan(x + y).
sin y = - 2/3, cos x = -1/5, x in quadrant II, y in quadrant III
Open Question
Use the given information to find the quadrant of x + y.
sin y = - 2/3, cos x = -1/5 , x in quadrant II, y in quadrant III
Open Question
Use the given information to cos(x - y).
cos x = 2/9, sin y = -1/2, x in quadrant IV, y in quadrant III