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    A curve, C, has parametric equations
    x = sinθ - cosθ + 1
    y = sin2θ
    Show that the cartesian equation of the curve is y = - x^2 + 2x

    Could someone show the working for this? :confused:
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    y= 2sinθcosθ
    y= 1 - (sinθ - cosθ )²
    = 1 - (x-1)²
    = -x² + 2x
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    (Original post by C4>O7)
    y= 2sinθcosθ
    y= 1 - (sinθ - cosθ )²
    = 1 - (x-1)²
    = -x² + 2x
    how did you get to the second step?
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    x = sinθ - cosθ + 1
    y = sin2θ = 2sinθcosθ

    x-1 = sinθ - cosθ
    (x-1)² = (sinθ - cosθ )²
    x² - 2x + 1 = -2sinθcosθ + sin²θ + cos²θ
    x² - 2x + 1 = -2sinθcosθ + 1
    x² - 2x = -2sinθcosθ
    -x² +2x = 2sinθcosθ

    y = -x² + 2x
 
 
 
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