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Math Help - Solving for x with a trig function

  1. #1
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    Solving for x with a trig function

    How do I solve for x when f = 4(-cos^2(x) + sin^2(x) + sin(x))?

    I can regroup the function in various ways, and I factored out the 4 already, but I don't know how get the function so that I can solve for x... If you get me started on the right path, or hint at an identity that I can use, that would help. Thanks.
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  2. #2
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    e^(i*pi)'s Avatar
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    Quote Originally Posted by Maziana View Post
    How do I solve for x when f = 4(-cos^2(x) + sin^2(x) + sin(x))?

    I can regroup the function in various ways, and I factored out the 4 already, but I don't know how get the function so that I can solve for x... If you get me started on the right path, or hint at an identity that I can use, that would help. Thanks.
    -cos^2(x) = -(1-sin^2(x)) = sin^2(x)-1

    <br />
4(sin^2(x)-1+sin^2(x)+sin(x)) = 4(2sin^2(x)+sin(x)-1)

    This is now a quadratic in sin(x)
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  3. #3
    Senior Member pacman's Avatar
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    f(x) = 4(-cos^2(x) + sin^2(x) + sin(x)) = 4(2sin^2(x)+sin(x)-1),

    y = f(x) = 4(2sin^2(x)+sin(x)-1), or 4(2sin^2(x)+sin(x)-1) = 0 if you want to solve for the roots.

    USE QUADRATIC FORMULA: solve for x then, . . . . see graph of the function

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