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

1. ## "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.

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

$\displaystyle \sin^4{x} =$

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

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

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

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

finish by cleaning up the last expression

3. Thanks!

These identities are kicking my butt.

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# sin 4x in terms of sin x

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