SOLUTION: Let f (x) = (1/(x^2 sqrt(49 + x^2))
and g(t) = 7 tan (t)
for 0 < t < pi/2
Find (f º g)(t) and simplify so that there are no radicals in the function. Write your answer in t
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-> SOLUTION: Let f (x) = (1/(x^2 sqrt(49 + x^2))
and g(t) = 7 tan (t)
for 0 < t < pi/2
Find (f º g)(t) and simplify so that there are no radicals in the function. Write your answer in t
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Question 929358: Let f (x) = (1/(x^2 sqrt(49 + x^2))
and g(t) = 7 tan (t)
for 0 < t < pi/2
Find (f º g)(t) and 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) =
THANKS!
Please explain
THANKS! Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! Let f (x) = (1/(x^2 sqrt(49 + x^2))
and g(t) = 7 tan (t) for 0 < t < pi/2
Find (f º g)(t) and 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) = f[g(t)] = f[7*tan(t)]
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= 1/[(7tan(t))^2*sqrt(49 + (7*tan(t))^2)]
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= 1/[49tan^2(t)*sqrt(49 + 49tan^2(t)]
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= 1/[49tan^2(t)*7sqrt(1+tan^2(t)]
= 1/[49tan^2(t)*7sec(t)]
= 1/[343 *sin^2(t)/cos^3(t)]
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Cheers,
Stan H.
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