Trig Functions: Find f(g(t)) for g(t) = 10/8 csc(t), f(x) =

[snakeyesxlaw]

Let g(t) = 10/8 csc(t) for 0 < t < (pi)/2 and

f(x)=((64 x^2 - 100)^(3/2))/x .

Find f (g(t)) and simplify. Your answer should not contain any radicals. After simplifying your answer. In sin (t) cos(t)

f (g(t)) = ?

far as i know,

square-root of (64 * (10/8 csc (t))^2 - 100)^3 divided by 10/8 csc (t)

any suggestions?

 

[skeeter]

start by squaring (10/8)*csc(t) ... you should see that the 64 will cancel, and the 100 can be factored out from the two remaining terms inside.

you'll use the identity csc²(t) - 1 = cot²(t)

make the struggle to do the algebra.

you should finally get f[g(t)] = 800cos³(t)/sin²(t)