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the right triangle shown, explain why v = (π/2) - u. Explain how you can obtain all six cofunction identities from this triangle for 0 < u < π/2. sin(u) = b = с te that u and v are complementary angles. So the cofunction identities state that "a trigonometric function of an angle u is equal to the corresponding cofunction of the Label the side opposite v as a, the side opposite u as b, and the hypotenuse as c. Since u + v + = π, u + v = 1 and v= Next, express all six trigonometric functions for each angle. cos(u) = = sin(-u) tan(u) = sec(u) = £= a csc(u) = 11 cot(u) == C a V = sin(v) = cos(u) = sin = = sin(u) = cos(-u) cot(v) =tan(u) = cot(- -) ⇒ sec(u) = csc(-u) = sec(v) ⇒ csc(u) = sec(-u) cot(u) = tan X

the right triangle shown, explain why v = (π/2) - u. Explain how you can obtain all six cofunction identities from this triangle for 0 < u < π/2. sin(u) = b = с te that u and v are complementary angles. So the cofunction identities state that "a trigonometric function of an angle u is equal to the corresponding cofunction of the Label the side opposite v as a, the side opposite u as b, and the hypotenuse as c. Since u + v + = π, u + v = 1 and v= Next, express all six trigonometric functions for each angle. cos(u) = = sin(-u) tan(u) = sec(u) = £= a csc(u) = 11 cot(u) == C a V = sin(v) = cos(u) = sin = = sin(u) = cos(-u) cot(v) =tan(u) = cot(- -) ⇒ sec(u) = csc(-u) = sec(v) ⇒ csc(u) = sec(-u) cot(u) = tan X

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.2: Trigonometric Functions Of Angles
Problem 91E
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In the right triangle shown, explain why v = (π/2) - u. Explain how you can obtain all six cofunction identities from this triangle for 0 < u < 1/2. Note that u and v are complementary angles. So the cofunction identities state that "a trigonometric function of an angle u is equal to the corresponding cofunction of the complementa Label the side opposite v as a, the side opposite u as b, and the hypotenuse as c. Since u + v + TL = 16₂ u+v= 1 Next, express all six trigonometric functions for each angle. cos(u) = = sin(v) = cos(u) = sin(- -) = sin(u) = cos(-u) = cot(v) =tan(u) = cot(-u) sin(u) = b = tan(u) = sec(u) = £ = csc(u) = 11 cot(u) = = = C a b ⇒ sec(u) = = CSC ( 1/2 - U) = sec(v) => csc(u) = sec(-u) =tan(-u) ⇒ cot(u) = X and y= u.
Transcribed Image Text:In the right triangle shown, explain why v = (π/2) - u. Explain how you can obtain all six cofunction identities from this triangle for 0 < u < 1/2. Note that u and v are complementary angles. So the cofunction identities state that "a trigonometric function of an angle u is equal to the corresponding cofunction of the complementa Label the side opposite v as a, the side opposite u as b, and the hypotenuse as c. Since u + v + TL = 16₂ u+v= 1 Next, express all six trigonometric functions for each angle. cos(u) = = sin(v) = cos(u) = sin(- -) = sin(u) = cos(-u) = cot(v) =tan(u) = cot(-u) sin(u) = b = tan(u) = sec(u) = £ = csc(u) = 11 cot(u) = = = C a b ⇒ sec(u) = = CSC ( 1/2 - U) = sec(v) => csc(u) = sec(-u) =tan(-u) ⇒ cot(u) = X and y= u.
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