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1. Using the substitution 0 = 2 arctant, it is possible to transform any rational function of trig functions into a rational function of t, and hence use partial fractions. In this problem, you will use this substitution to find an antiderivative of 1 sin cos (a) Using the double-angle identity cos(24) t 2 tan = , show that cos 0 = 2 ² ( √1 + p) ² - 1 - 1 - 0²/² 1+t2 = (c) Find an expression for de in terms of dt. (b) By using a double-angle identity for sine, find a similar formula for sin 8. 2(cos)2-1, and a triangle representing (d) Using your results above, compute the integral 15 sin 8 cos 8 do.

1. Using the substitution 0 = 2 arctant, it is possible to transform any rational function of trig functions into a rational function of t, and hence use partial fractions. In this problem, you will use this substitution to find an antiderivative of 1 sin cos (a) Using the double-angle identity cos(24) t 2 tan = , show that cos 0 = 2 ² ( √1 + p) ² - 1 - 1 - 0²/² 1+t2 = (c) Find an expression for de in terms of dt. (b) By using a double-angle identity for sine, find a similar formula for sin 8. 2(cos)2-1, and a triangle representing (d) Using your results above, compute the integral 15 sin 8 cos 8 do.

Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter10: Systems Of Equations And Inequalities
Section10.3: Partial Fractions
Problem 2E
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1. Using the substitution 0-2 arctant, it is possible to transform any rational function of trig functions into a rational function of t, and hence use partial fractions. In this problem, you will use this substitution to find an antiderivative of 1 sin cos (a) Using the double-angle identity cos(24) tan y = show that cos 0 = 2 1 2 (AT)* = 2(cosp)21, and a triangle representing 2 (c) Find an expression for de in terms of dt. -1= (b) By using a double-angle identity for sine, find a similar formula for sin 0. 1-t² 1+ t2 1 sin cos (d) Using your results above, compute the integral S do. FESE Partly clou
Transcribed Image Text:1. Using the substitution 0-2 arctant, it is possible to transform any rational function of trig functions into a rational function of t, and hence use partial fractions. In this problem, you will use this substitution to find an antiderivative of 1 sin cos (a) Using the double-angle identity cos(24) tan y = show that cos 0 = 2 1 2 (AT)* = 2(cosp)21, and a triangle representing 2 (c) Find an expression for de in terms of dt. -1= (b) By using a double-angle identity for sine, find a similar formula for sin 0. 1-t² 1+ t2 1 sin cos (d) Using your results above, compute the integral S do. FESE Partly clou
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