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

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 � g)(t) in

Question 926160: Please help, so confused on how to solve this.
Let
for
and
f(x) =
Find (f � g)(t) in terms of sin(t) and cos(t) and simplify so that it does not contain any radicals.
(f � g)(t) =
THANKS
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Let g(t) = (2/7) csc(t)
for
and
f(x) = (49x^2 - 4)^(3/2)/(x)
Find (f � g)(t) in terms of sin(t) and cos(t) and simplify so that it does not contain any radicals in the denominator.
(f � g)(t) = f[(2/7)csc(t)] = 49(4/49)csc^2(t)^(3/2)/[(2/7csc(t)]
=====
= (4/(2/7)csc^(1/2)(t)
-----
= 14*(1/(sin^(1/2)(t)))
----
= 14*(sin^(1/2)(t)/sin(t))
-------------------------
Cheers,
Stan H.
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