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

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    "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.
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    Quote Originally Posted by Wolvenmoon View Post
    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 =<br />

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

    \frac{1}{4}\left[1 - 2\cos(2x) + \cos^2(2x)\right] =<br />

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

    finish by cleaning up the last expression
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  3. #3
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    Thanks!

    These identities are kicking my butt.
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