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Math Help - Trig Function

  1. #1
    Junior Member
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    Trig Function

    How to solve this trig function 2cos(3x)=1 for all the values of x: \frac{-\pi}{6}\leq{x}\leq\frac{5\pi}{6}

    can someone please demonstrate how would I solve such problems step by step? I'm still trying to get my head around these trig functions.
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  2. #2
    Super Member Random Variable's Avatar
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    2cos(3x)=1

     cos(3x)= \frac{1}{2}

     cos^{-1}(cos(3x)) = cos^{-1}(\frac {1}{2})

     3x = cos^{-1}( \frac {1}{2})

    You want to find the angle (or angles) in the range given whose cosine is 1/2. There are two angles:  \frac{\pi}{3} and  -\frac{\pi}{3}

    so  3x = \pm \frac{\pi}{3}

    or x = \pm \frac{\pi}{9}
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  3. #3
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    Dont forget that if possible the angle may be +or- 2*pi within the domain
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