Question

Trig Question...with failed attempt :/
Attachments to follow.

Answer 1

Here's the question:

Answer 2

And here's my attempt:

Answer 3

I have a feeling that when i substituted sin(pi/2 - x) for cos that's when things started going bad...

Answer 4

better write cos x as \(\sqrt{1-sin^2 x}\).
then h(y) will be -2y\(\sqrt{1-y^2}\)

Answer 5

Alright... then how do i use that to find g?

Answer 6

u wanted to find h
g u already found as -2sin x cos x

Answer 7

but do you use g(y) or g(x)? I'm a little confused on this end part...

Answer 8

u are correct when u put y=sin x
so that h is function of y.
let g remain as the function of x only.

Answer 9

so, am i solving for g(x)= h(f(y)) or g(x)= h(f(x))?

Answer 10

g(x)= h(f(x))
the replace y= f(x)=sin x
which u have correctly done.

Answer 11

so, would the answer just be g(x) = -2sin(x) SQRT(1-sin^2(x))?

Answer 12

wait... i just messed up... i'm looking for g(x)

Answer 13

u wanted to fin h(y) isn't it ?

Answer 14

yeah... sorry i just got mixed up there

Answer 15

g(x) u found correctly as -2sin x cos x

Answer 16

Alright! I finally understand it! Sorry i was slow... i just needed to stare at it for awhile!
Thanks so much for all your help! :D

Answer 17

welcome :)