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Thread: Random Trig Problems

  1. #1
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    Random Trig Problems

    Getting hung up on some trig-solving...

    For the first problem here, we get 8x-2sec^2(x) when derived and then you set that equal to 0 to find the critical points. I have no clue at all how to solve that.

    The second, you get -8sin(x)+4cos^2(x) when taking the derivative. Again, set it equal to 0 and then I'm stumped.

    Feels bad that this is just algebra, but I dunno what to do. Will greatly appreciate any help!
    Attached Thumbnails Attached Thumbnails Random Trig Problems-1.png   Random Trig Problems-2.png  
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  2. #2
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    Re: Random Trig Problems

    solve for x: 8x=2sec^2 x - Wolfram|Alpha Results

    http://m.wolframalpha.com/input/?i=s...x%3D4cos%5E2+x

    These have no rational solutions. You need a computer algebra system to find critical points.

    You could simplify the second one to:
    \sin^2 x+2\sin x-1=0 \Longrightarrow \sin x = -1\pm \sqrt{2}
    Last edited by SlipEternal; Nov 30th 2017 at 05:20 PM.
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  3. #3
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    Re: Random Trig Problems

    That helped for 9, still can't get 13, though.
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  4. #4
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    Re: Random Trig Problems

    That's because \dfrac{d}{dx}(8\cos x+4\sin^2 x)=-8\sin x +8\sin x \cos x

    When you set that to zero, you get \sin x (\cos x -1) =0

    So x=-\pi , 0 ,\pi
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