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Math Help - Help to solve simple trigonometric equation

  1. #1
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    Help to solve simple trigonometric equation

    Here's the equation: cos^2 ѳ-cos ѳ=2
    I usually apply this set of method to solve such questions but it doesn't seem to work out this time round:
    1)Identify quadrant
    2)Find basic angle
    3)Adjust domain
    4)Find values of ѳ
    If you see what i mean.
    Anyway, please do help out.
    Thanks in advance!
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  2. #2
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    \cos^2{\theta} - \cos{\theta} = 2

    \cos^2{\theta} - \cos{\theta} - 2 = 0

    (\cos{\theta} + 1)(\cos{\theta} - 2) = 0

    \cos{\theta} + 1 = 0 or \cos{\theta} - 2 = 0

    \cos{\theta} = -1 or \cos{\theta} = 2.


    Since -1 \leq \cos{\theta} \leq 1 for all \theta, that means the second equation is impossible.

    So \cos{\theta} = -1

    \theta = \pi + 2\pi n where n \in \mathbf{Z}.
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  3. #3
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    Cheers for your quick reply!
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