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Math Help - Solving Tangent Equation

  1. #1
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    Solving Tangent Equation

    Hello M.H.F.

    I am looking for suggestions on how to solve this Tangent Equation:

    tan(x) = -sqrt(3) for [0,2pi]

    I can solve this using my graphing calculator by graphing y1 = tan(x) and y2 = -sqrt(3) and using the intersect function to get my answers of 2pi/3 and 5pi/3.

    I am really interested to see how I would go about solving this mathematically without graphing. Please advise or show any techniques that you find appropriate.

    Thanks,
    Jack Daniels
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  2. #2
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    Quote Originally Posted by UC151CPR View Post
    Hello M.H.F.

    I am looking for suggestions on how to solve this Tangent Equation:

    tan(x) = -sqrt(3) for [0,2pi]

    I can solve this using my graphing calculator by graphing y1 = tan(x) and y2 = -sqrt(3) and using the intersect function to get my answers of 2pi/3 and 5pi/3.

    I am really interested to see how I would go about solving this mathematically without graphing. Please advise or show any techniques that you find appropriate.

    Thanks,
    Jack Daniels
    \tan{x} = -\sqrt{3} is a unit circle value.

    for 0 \le x < 2\pi ...

    \tan\left(\frac{2\pi}{3}\right) = -\sqrt{3}

    and

    \tan\left(\frac{5\pi}{3}\right) = -\sqrt{3}
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