%3D In the right triangle shown, explain why v = (x/2)- u. Explain how you can obtain all six cofuncti %3D Note that u and v are complementary angles. So the cofunction identities state that "a trigonometri- Label the side opposite v as a, the side opposite u as b, and the hypotenuse as c. Since u + Next, express all six trigonometric functions for each angle. sin - u) cos(u) = sin(v) » cos(u) %3D %3D co(-u) sin(u) : - sin(u) = cos %3D tan(u) = cot(v) = tan(u) = cot-u) %3D %3D sec(u)3D등- - sec(u) = cse( -u) %3! = CS csc(u) = sec(v) csc(u) = sec %3D cot(u) = - cot(u) = tan-u) %3D

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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In the right triangle shown, explain whyv (x/2)-u. Explain how you can obtain all six cofunction identities from this triangle for 0 <u< T/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 complementary angle
Label the side opposite v as a, the side opposite u as b, and the hypotenuse as c. Since u + v +
I, u+v=
and v =
-U.
Next, express all six trigonometric functions for each angle.
cos(u) =
= sin(v) cos(u) = sin
- sin(u) = cos- u)
sin(u) =
=COS
co-)
tan(u) =
cot(v) tan(u) = co
sec(u) = =
→sec(u)-csc(즉-)
= sec(v)
- csc(u) = sec-u)
csc(u) =
%3D
cot(u) =
= cot(u)
= tan
Transcribed Image Text:In the right triangle shown, explain whyv (x/2)-u. Explain how you can obtain all six cofunction identities from this triangle for 0 <u< T/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 complementary angle Label the side opposite v as a, the side opposite u as b, and the hypotenuse as c. Since u + v + I, u+v= and v = -U. Next, express all six trigonometric functions for each angle. cos(u) = = sin(v) cos(u) = sin - sin(u) = cos- u) sin(u) = =COS co-) tan(u) = cot(v) tan(u) = co sec(u) = = →sec(u)-csc(즉-) = sec(v) - csc(u) = sec-u) csc(u) = %3D cot(u) = = cot(u) = tan
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