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Math Help - Polar Curves and Arc Lengths

  1. #1
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    Polar Curves and Arc Lengths

    Given the polar equation:

    r= theta + sin(3theta), theta is greater than or equal to 0 and less than or equal to pi,

    Determine the angle which corresponds with the x-coordinate, 3.

    OK, so I tried to solve this using the formula such as r^2= x^2 +y^2 ,x=rcos(theta), y=rsin(theta), tan(theta)=y/x ,but I ended up with a really long equation.

    Sorry that everything is written out. I don't know how to write the equations using the actual notation.

    Help, please?
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    If (3,y) belongs to the curve then,

    \sqrt{9+y^2}=\arctan (y/3)+\sin(\arctan (y/3))

    The left side has absolute value \geq 3 and the right side \leq \pi/2+1<3 . So, there is no solution.


    Fernando Revilla
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