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Math Help - Help with Trigonometric Identities

  1. #1
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    Help with Trigonometric Identities

    Sorry for another one but this one is giving me a lot of trouble.

    sin^3{x}cos^2{x}=cos^2{x}sin{x}-cos^4{x}sin{x}

    I assume you would start with the right side since it's the harder side.
    I tried changing cos^2{x}\Rightarrow1-sin^2{x} from the RHS, but end up no where. I'm confused at what I should just keep and what I should change with the identity:

    cos^2{x}+sin^2{x}=1

    Edit: Didn't realize there was a sub forum specifically for Trigonometry. Can I move this thread?
    Last edited by toeknee; February 16th 2011 at 05:15 PM.
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  2. #2
    MHF Contributor Also sprach Zarathustra's Avatar
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    Quote Originally Posted by toeknee View Post
    Sorry for another one but this one is giving me a lot of trouble.

    sin^3{x}cos^2{x}=cos^2{x}sin{x}-cos^4{x}sin{x}

    I assume you would start with the right side since it's the harder side.
    I tried changing cos^2{x}\Rightarrow1-sin^2{x} from the RHS, but end up no where. I'm confused at what I should just keep and what I should change with the identity:

    cos^2{x}+sin^2{x}=1

    Edit: Didn't realize there was a sub forum specifically for Trigonometry. Can I move this thread?


    cos^2{x}sin{x}-cos^4{x}sin{x}=cos^2{x}sin{x}(1-cos^2{x})=cos^2{x}sin{x}sin^2{x}=cos^2{x}sin^3{x}
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  3. #3
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    How does cos^4{x}sin{x} change to 1-cos^2{x}?
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  4. #4
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    It doesn't "change". He factored out \cos^2 x \sin x since it's common to both terms.

    In general, ab+ac=a(b+c)
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  5. #5
    MHF Contributor Also sprach Zarathustra's Avatar
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    Quote Originally Posted by toeknee View Post
    How does cos^4{x}sin{x} change to 1-cos^2{x}?
    It's not. I just pulled out cos^2{x}sin{x} from cos^2{x}sin{x} and cos^4{x}sin{x}=cos^2{x}cos^2{x}sin{x}
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