Textbook 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
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6. Trigonometric Identities and More Equations
Sum and Difference Identities
Back6. Trigonometric Identities and More Equations
Sum and Difference Identities
- Textbook QuestionIn 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 2603views
- Textbook QuestionIn Exercises 69–74, rewrite each expression as a simplified expression containing one term.sin (α - β) cos β + cos (α - β) sin β784views
- Textbook 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
593views - Textbook 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
583views - Textbook 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
622views - Textbook 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
664views - Textbook Question
Use the given information to find tan(x + y).
cos x = 2/9, sin y = -1/2, x in quadrant IV, y in quadrant III
546views - Textbook Question
Use the given information to find the quadrant of x + y.
cos x = 2/9, sin y = -1/2, x in quadrant IV, y in quadrant III
580views - Textbook Question
Verify that each equation is an identity.
sin(x + y) + sin(x - y) = 2 sin x cos y
596views - Textbook Question
Verify that each equation is an identity. See Example 4.
tan(x - y) - tan(y - x) = 2(tan x - tan y)/(1 + tan x tan y)
624views - Textbook Question
Verify that each equation is an identity.
sin(s + t)/cos s cot t = tan s + tan t
568views - Textbook Question
Verify that each equation is an identity.
sin(x + y)/cos(x - y) = (cot x + cot y)/(1 + cot x cot y)
609views - Textbook Question
Verify that each equation is an identity.
(tan(α + β) - tan β)/(1 + tan(α + β) tan β) = tan α
635views - Textbook Question
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
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