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Math Help - Polar coordinates

  1. #1
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    Question Polar coordinates

    Hey, I need help!!! Could anyone help me to solve this? I need to change this functions to polar ant than I have to calculate area which limited by two curves....


    Thank you!!! Polar coordinates-task.jpg
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  2. #2
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    Re: Polar coordinates

    I don't see a function, I see an equation. Do you want to solve this equation for $r=\sqrt{x^2+y^2}$ ?
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  3. #3
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    Re: Polar coordinates

    Hello, raplys!

    I need to change this function to polar: . (x^2+y^2)^2 \:=\:a^2(x^2+2y^2)

    and then I have to calculate area which limited by two curves. . What two curves?

    Conversions: . \begin{Bmatrix} x \:=\:r\cos\theta \\ y \:=\:r\sin\theta \\ x^2+y^2 \:=\:r^2 \end{Bmatrix}

    We have: . (x^2+y^2)^2 \:=\:a^2(x^2+2y^2)

    . . . . . . . . (x^2+y^2)^2 \:=\:a^2(x^2+y^2 + y^2)

    . . . . . . . . . . . . (r^2)^2 \;=\;a^2 ( r^2 + r^2\sin^2\!\theta)

    . . . . . . . . . . . . . . r^4 \;=\;a^2r^2(1 + \sin^2\!\theta)

    . . . . . . . . . . . . . . r^2 \;=\;a^2(1+\sin^2\!\theta)

    . . . . . . . . . . . . . . . r \;=\;\pm\:\!a\sqrt{1 + \sin^2\!\theta}
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