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Math Help - trig max/min values

  1. #1
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    trig max/min values

    hi im struggling with my homework and was wondering if anyone can help

    here the question...

    find the max and min values of 3sinx + 2cosx ,and find in radians ,the smallest values of x at which they occur

    any help is fully appreciated thank you
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  2. #2
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    \frac{d}{dx}[3sin(x)+2cos(x)]=3cos(x)-2sin(x)

    Set to 0 and solve for x:

    3cos(x)-2sin(x)=0

    Now, assuming cos(x)\neq 0:

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

    tan(x)=\frac{3}{2}

    x=C{\pi}-tan^{-1}(\frac{2}{3})+\frac{\pi}{2}

    Let C=0 for the smallest value for the max and C=-1 for the smallest value that is a min.

    Graph it as well and take a peek.
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