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Math Help - Trig inequality?

  1. #1
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    Trig inequality?

    How would I go about solving |\cos x|^{1+\sin x+\cos x} \geq 1? All help is welcome.
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    By THINKING, not using "formulas"!

    You know that |cos(x)| is always less than or equal to 1. You also know that powers of a number between 0 and 1 are always smaller than the number itself: if 0< y< 1 then y^n< y.

    Saying that an absolute value of a power of cos(x) is "greater than or equal to 1" is exactly the same as saying it is equal to 1. And so the power itself is equal to either 1 or -1. That can only happen when the base is 1 or -1. For what x is cos(x)= 1 or cos(x)= -1?
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  3. #3
    MHF Contributor Also sprach Zarathustra's Avatar
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    Quote Originally Posted by atreyyu View Post
    How would I go about solving |\cos x|^{1+\sin x+\cos x} \geq 1? All help is welcome.
    You also can write it in the following form:


    cos^2(x)^{\frac{1}{2}( sin(x)+cos(x)+1)} \geq1
    Last edited by Also sprach Zarathustra; November 20th 2010 at 05:06 AM.
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  4. #4
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    Actually there are more values of x than Prof Halls gave.
    If 1+\sin(x)+\cos(x)<0 then the given inequality holds.
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