SOLUTION: Composite trig function problem? Let f(x) = 4x/(&#8730;(1-x^2)) and g(t) = sin t for 0 < t < &#960;/2 simplify so that there are no radicals in the function. Write your answer

Algebra ->  Trigonometry-basics -> SOLUTION: Composite trig function problem? Let f(x) = 4x/(&#8730;(1-x^2)) and g(t) = sin t for 0 < t < &#960;/2 simplify so that there are no radicals in the function. Write your answer       Log On


   

Question 923776: Composite trig function problem?
Let f(x) = 4x/(√(1-x^2)) and g(t) = sin t for 0 < t < π/2
simplify so that there are no radicals in the function. Write your answer in terms of sin(t) and cos(t).
(f º g)(t) =

Thank you
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
(f º g)(t) is the same as f%28g%28t%29%29


0+%3C+t+%3C+pi%2F2 which means t is in quadrant I


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f%28x%29+=+%284x%29%2F%28sqrt%281-x%5E2%29%29 Start with f(x)


f%28g%28t%29%29+=+%284%2Ag%28t%29%29%2F%28sqrt%281-%28g%28t%29%29%5E2%29%29 Replace every x with g(t)


f%28g%28t%29%29+=+%284%2Asin%28t%29%29%2F%28sqrt%281-%28sin%28t%29%29%5E2%29%29 Replace every g(t) on the right side with sin%28t%29


f%28g%28t%29%29+=+%284%2Asin%28t%29%29%2F%28sqrt%28%28cos%28t%29%29%5E2%29%29 Use a trig identity


f%28g%28t%29%29+=+%284%2Asin%28t%29%29%2F%28cos%28t%29%29 Take the square root. t is in quadrant I, so cos%28t%29 is positive.

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