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Math Help - Cartesian and Polar Equations

  1. #1
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    Cartesian and Polar Equations

    1. Identify the curve: r*cos(theta) = 1 by finding a Cartesian equation for the curve.

    2. Identify the curve: r = tan(theta)*sec(theta) by finding a Cartesian equation for the curve.

    3. Find a polar equation for the curve represented by xy = 4.

    Thanks for the help.
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  2. #2
    MHF Contributor
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    Quote Originally Posted by eigenvector11 View Post
    1. Identify the curve: r*cos(theta) = 1 by finding a Cartesian equation for the curve.

    2. Identify the curve: r = tan(theta)*sec(theta) by finding a Cartesian equation for the curve.

    3. Find a polar equation for the curve represented by xy = 4.

    Thanks for the help.
    by "Cartesian", I assume rectangular or (x,y).

    x = r*cosT ------------cosT = x/r
    y = r*sinT-----------------sinT = y/r
    r = sqrt(x^2 +y^2)


    1) r*cosT = 1
    That is x = 1 -----------a vertical line, answer.

    2) r = tanT*secT
    r = sinT/cosT *1/cosT
    r = sinT / cos^2(T)
    r = (y/r) / (x/r)^2
    r = ry / x^2
    1 = y / x^2
    x^2 = y
    y = x^2 -------a vertical parabola that opens upward, answer.

    3) xy = 4
    (r*cosT)(r*sinT) = 4
    (r^2)(sinTcosT) = 4
    (r^2)((1/2)sin(2T)) = 4
    (r^2)sin(2T) = 8
    r^2 = 8/sin(2T)
    r^2 = 8csc(2T)
    r = 2sqrt[2csc(2T)] -----------answer.
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