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Math Help - General Solutions to Equations...

  1. #1
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    Question General Solutions to Equations...

    How can I find the general solutions to the following equations where 0 < x < 2pi?

    2cos^2x + cosx = 1

    2tanx + square root of 12 = 0

    Thanks.
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  2. #2
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    Quote Originally Posted by oryxncrake View Post
    How can I find the general solutions to the following equations where 0 < x < 2pi?

    2cos^2x + cosx = 1

    \textcolor{red}{2\cos^2(x) + \cos(x) - 1 = 0}<br />

    \textcolor{red}{[2\cos(x) - 1][\cos(x) + 1] = 0}

    set each factor = 0 and solve for cosx ... solutions for x will be unit circle values


    2tanx + square root of 12 = 0

    \textcolor{red}{2\tan(x) + 2\sqrt{3} = 0}

    \textcolor{red}{\tan(x) = -\sqrt{3}}

    look for solutions on your unit circle
    ...
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