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Math Help - Trigonometry quest.

  1. #1
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    Trigonometry quest.

    Hello.

    a- Express 5sinx+ 12cosx in the form Rsin(x+A)

    a- Find the Maximum and Minimum values of f(x) where
    f(x)= 1 / ( 5sinx+12cosx+17). State also the values of x in the range of x is greater than 0 less than 360 degrees, at which they occur.

    I can do part a) My answer is 13sin(x+67,4)
    But i cant do part b)

    Thanks.
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  2. #2
    MHF Contributor
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    Quote Originally Posted by Oasis1993 View Post
    Hello.

    a- Express 5sinx+ 12cosx in the form Rsin(x+A)

    a- Find the Maximum and Minimum values of f(x) where
    f(x)= 1 / ( 5sinx+12cosx+17). State also the values of x in the range of x is greater than 0 less than 360 degrees, at which they occur.

    I can do part a) My answer is 13sin(x+67,4)
    But i cant do part b)

    Thanks.
    HI

    your first part is correct .

    (b) \frac{1}{5\sin x+12\cos x+17}=\frac{1}{13\sin (x+67.4^o)+17}

    Note that sin is max and min at 1 and -1 respectively .

    For f(x) to be max , its denominator has to be min and vice versa .

    You can also find the corresponding value of x , depending whether you are taking 1 or -1 for your sin .
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