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Trigonometry

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What value(s) of theta solve the following equation? cos^2(theta)-cos(theta)-6=0?

I try plugging in different numbers but I am not sure exactly what I am looking for in order to solve?

  • Trigonometry -

    cos^2 Ø - cosØ - 6 = 0

    let cosØ = x , then we get

    x^2 - x - 6 = 0
    (x-3)(x+2) = 0
    x = 3 or x = -2
    then cosØ = 3 or cosØ = -2

    both of these are not possible, since the cosine is defined only between -1 and +1

    there is no solution to your equation

  • Trigonometry -

    also, you coul dhave reasoned thus:

    cos^2θ <= 1
    -1 <= cosθ <= 1

    no way could you have cos^2θ - cosθ = 6

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