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Math Help - help on parametr equation i cant do it at all

  1. #1
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    help on parametr equation i cant do it at all

    x=Acos^3t , y= Asin^3t

    where A is a positive constant and 0<t<0.5pie

    1 express dy/dx in terms of t

    2 show that equation of the tangent to the curve at the point with parameter t is

    Xsint + ycost = Asint times cost

    extra question based on this

    hence show that, if tangent meets the x axis at X and the Y axis at Y then the length of XY is always equal to A
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by vserian View Post
    x=Acos^3t , y= Asin^3t

    where A is a positive constant and 0<t<0.5pie

    1 express dy/dx in terms of t

    2 show that equation of the tangent to the curve at the point with parameter t is

    Xsint + ycost = Asint times cost

    extra question based on this

    hence show that, if tangent meets the x axis at X and the Y axis at Y then the length of XY is always equal to A
    \frac{dy}{dx}=\frac{dy}{dt}\frac{dt}{dx}

    Now differentiate the first equation with respect to x to find \frac{dt}{dx} and the second by t to find \frac{dy}{dt} and the first part is done.

    CB
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