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trig

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solve the equation of the domain 0¡Ü¦È¡Ü2¦Ð
3cos^2theta - 5costheta -1 = 3sin^2theta

  • trig - ,

    3 cos ^ 2 theta - 5 cos theta - 1 - 3 sin ^ 2 theta = 0

    3 cos ^ 2 theta - 5 cos theta - 1 - 3 ( 1 - cos ^ 2 theta ) = 0

    3 cos ^ 2 theta - 5 cos theta - 1 - 3 + 3 cos ^ 2 theta = 0

    6 cos ^ 2 theta - 5 cos theta - 4 = 0

    Substitute :

    u = cos theta

    6 u ^ 2 - 5 u - 4 = 0

    The exact solutons are :


    u = cos teta = 4 / 3 = 1.333

    and

    u = cos theta = - 1 / 2


    cosine can't be great of 1

    so the solutions are :

    cos theta = - 1 / 2


    theta = ( 2 / 3 ) pi = 120 °

    and

    theta = ( 4 / 3 ) pi = 240 °




    If you don't know hov to solve equation:

    6 u ^ 2 - 5 u - 4 = 0


    In google type:

    quadratic equation online

    When you see list of results click on:

    Free Online Quadratic Equation Solver:Solve by Quadratic Formula

    When page be open in rectangle type:

    6 u ^ 2 - 5 u - 4 = 0

    and click option: solve it!

    You wil see solution step-by-step

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