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Math Help - Moving onto trigo equations :(

  1. #1
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    Moving onto trigo equations :(

    equation of a line is  y = 3sin2x + 2cos^2x where 0 < X < 360

    Calculate value for which the curve

    a) meets the x-axis b) meets the line y = 2

    I know that I have to simplify the equation and sub in y=0 and y=2, however I can't solve the equation.. thanks in advance!
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  2. #2
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    Quote Originally Posted by Punch View Post
    equation of a line is  y = 3sin2x + 2cos^2x where 0 < X < 360

    Calculate value for which the curve

    a) meets the x-axis b) meets the line y = 2

    I know that I have to simplify the equation and sub in y=0 and y=2, however I can't solve the equation.. thanks in advance!
    0 \le x < 360


    3\sin(2x) + 2\cos^2{x} = 0

    3(2\sin{x}\cos{x}) + 2\cos^2{x} = 0

    2\cos{x}(3\sin{x} + cos{x}) = 0

    \cos{x} = 0 ... x = 90 , x = 270

    3\sin{x} = -\cos{x}<br />

    \tan{x} = -\frac{1}{3}

    x = \arctan\left(-\frac{1}{3}\right) + 180

    x = \arctan\left(-\frac{1}{3}\right) + 360



    3\sin(2x) + 2\cos^2{x} = 2

    3(2\sin{x}\cos{x}) = 2 - 2\cos^2{x}

    6\sin{x}\cos{x} = 2(1 - \cos^2{x})

    6\sin{x}\cos{x} = 2\sin^2{x}

    3\sin{x}\cos{x} - \sin^2{x} = 0

    \sin{x}(3\cos{x} - \sin{x}) = 0

    \sin{x} = 0 ... x = 0 , x = 180

    3\cos{x} = \sin{x}

    \tan{x} = 3

    x = \arctan(3)

    x = \arctan(3) + 180
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