SOLUTION: Please help, so confused on how to solve this. Let {{{ g(t) = (2/7) csc(t) }}} for {{{ 0 < t < pi/2 }}} and f(x) = {{{ (49x^2 - 4)^(3/2)/(x) }}} Find (f º g)(t) in

Algebra ->  Trigonometry-basics -> SOLUTION: Please help, so confused on how to solve this. Let {{{ g(t) = (2/7) csc(t) }}} for {{{ 0 < t < pi/2 }}} and f(x) = {{{ (49x^2 - 4)^(3/2)/(x) }}} Find (f º g)(t) in       Log On


   



Question 926160: Please help, so confused on how to solve this.
Let +g%28t%29+=+%282%2F7%29+csc%28t%29+
for +0+%3C+t+%3C+pi%2F2+
and
f(x) = +%2849x%5E2+-+4%29%5E%283%2F2%29%2F%28x%29+
Find (f º g)(t) in terms of sin(t) and cos(t) and simplify so that it does not contain any radicals.
(f º g)(t) =
THANKS

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Let g(t) = (2/7) csc(t)
for +0+%3C+t+%3C+pi%2F2+
and
f(x) = (49x^2 - 4)^(3/2)/(x)
Find (f º g)(t) in terms of sin(t) and cos(t) and simplify so that it does not contain any radicals in the denominator.
(f º g)(t) = f[(2/7)csc(t)] = 49(4/49)csc^2(t)^(3/2)/[(2/7csc(t)]
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= (4/(2/7)csc^(1/2)(t)
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= 14*(1/(sin^(1/2)(t)))
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= 14*(sin^(1/2)(t)/sin(t))
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Cheers,
Stan H.
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