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Parametric to Rectangular?

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find the rectangular eqaution of the curve whose parametric equations are x=5cos2T and y=-sin2T, where 0 is less than/equal to T which is less than/equal to 180

  • Parametric to Rectangular? -

    from x = 5cos 2T ---> cos 2T = x/5
    from y = -sin 2T ---> sin 2T = -y

    we know sin^2 2T + cos^2 2T= 1
    x^2 /25 + y^2 = 1

    x^2 + 25y^2 = 25

    (looks like we have an ellipse)

    test:
    let T = 30°
    x = 5cos60° = 5(1/2) = 5/2
    y = -sin60° = -√3/2

    sub into the rectangular...
    LS = 25/4 + 25(3/4) = 100/4 = 25

    let T = 19.6°
    x = 5cos39.2· = appr. 3.8747
    y = -sin39.2 = appr. -.6320
    LS = 3.8747^2 + 25(.6320)^2 = 24.99999
    looks promising.

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