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Math Help - Help me please with triogonometry:)thank you

  1. #1
    Member helloying's Avatar
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    Help me please with triogonometry:)thank you

    12 cos x - 5 sin x = R cos (x + 22.6)

    solve x in range 0 to 360 degrees
    (12 cos x- 5 sin x)^2

    Also, find the max and min value of eqn.

    Kindly explain it clearly because I actually got an explanation from somewhere but it is not clear. Thank you greatly for your help.God bless you.
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  2. #2
    MHF Contributor
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    The kind of structure you have on the left is very cooperative. It is simply transformed to the even more convenient form on the left.

    R = \sqrt{12^{2}+(-5)^{2}} = 13

    R = sqrt(12^2 + (-5)^2) = 13

    The angle is a little trickier, but simply written.

    theta = -atan(-5/12)

    Then just write the answer 13*cos(x-theta)
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