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Math Help - Evaluate

  1. #1
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    Evaluate

    Evaluate cot x, given that cot x=sin x?
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  2. #2
    MHF Contributor
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    cot(x) = sin(x)
    cos(x) / sin(x) = sin(x)
    cos(x) = sin^2(x)
    cos(x) = 1 -cos^2(x)
    cos^2(x) +cos(x) -1 = 0
    By the Quadratic Formula,
    cos(x) = {-1 +,-sqrt[1^2 -4(1)(-1)]} / 2(1)
    cos(x) = {-1 +,-sqrt(5)}/2

    When cos(x) = (1/2)[-1 +sqrt(5)] = 0.618 ----umm, golden ratio conjugate.
    angle x then is in the 1st and 4th quadrants.
    adjacent side = 0.618
    hypotenuse = 1
    opposite side = sqrt[1^2 -(0.618)^2] = +,-0.786178
    So, cot(x) = adj/opp = 0.618 / (+,-0.786178) = +,-0.786 -------answer.

    When cos(x) = (1/2)[-1 -sqrt(5)] = -1.618
    Cannot be. The minimum value of the cosine of any angle ios only (-1).
    So, reject this factor.
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