# "Find an equivelent expression for sin^4(X) in terms of function values of...

• Oct 13th 2009, 01:28 PM
Wolvenmoon
"Find an equivelent expression for sin^4(X) in terms of function values of...
Attached is the problem. The example problem that I get is rewriting cos(4X), which coincidentally was what I got for the actual assignment. I'm reviewing it now.

"Find an equivelent expression for sin^4(X) in terms of function values of the sine or cosine of x, 2x, or 4x raised to the first power."

The answer is 3/8 - (cos(2x))/2 + (cos(4x))/8

(I've attached an image where it's written clearer.)

I haven't the first clue what the first step to get to this answer is. My book is no help at all.
• Oct 13th 2009, 02:16 PM
skeeter
Quote:

Originally Posted by Wolvenmoon
Attached is the problem. The example problem that I get is rewriting cos(4X), which coincidentally was what I got for the actual assignment. I'm reviewing it now.

"Find an equivelent expression for sin^4(X) in terms of function values of the sine or cosine of x, 2x, or 4x raised to the first power."

The answer is 3/8 - (cos(2x))/2 + (cos(4x))/8

(I've attached an image where it's written clearer.)

I haven't the first clue what the first step to get to this answer is. My book is no help at all.

note that $\sin^2{u} = \frac{1-\cos(2u)}{2}$ and $\cos^2{u} = \frac{1+\cos(2u)}{2}$

$\sin^4{x} =$

$(\sin^2{x})^2 =
$

$\left(\frac{1-\cos(2x)}{2}\right)^2 =$

$\frac{1}{4}\left[1 - 2\cos(2x) + \cos^2(2x)\right] =
$

$\frac{1}{4}\left[1 - 2\cos(2x) + \frac{1+\cos(4x)}{2}\right]$

finish by cleaning up the last expression
• Oct 14th 2009, 01:38 PM
Wolvenmoon
Thanks!

These identities are kicking my butt.