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Math Help - problem with polar coordinates

  1. #1
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    problem with polar coordinates

    Give inequalities for and which describe the region below in polar coordinates
    Here is the graph
    http://mandelbrot.math.buffalo.edu/w...rob4image1.png

    The two arcs shown are circular, and the region is between the two arcs and between the -axis and line graphed, which is .

    so
    ?<r<? ?<=<=?

    Have no clue for this.
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  2. #2
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    Quote Originally Posted by dylan5188 View Post
    Give inequalities for and which describe the region below in polar coordinates
    Here is the graph
    http://mandelbrot.math.buffalo.edu/w...rob4image1.png

    The two arcs shown are circular, and the region is between the two arcs and between the -axis and line graphed, which is .

    so
    ?<r<? ?<=<=?

    Have no clue for this.
    r_1 = \sqrt{1 + \frac{1}{3}} = \frac{2}{\sqrt{3}}

    r_2 = \sqrt{4 + \frac{4}{3}} = \frac{4}{\sqrt{3}}

    \theta_1 = \arctan\left(\frac{1}{\sqrt{3}}\right) = \frac{\pi}{6}

    \theta_2 = \frac{\pi}{2}<br />

    A = \int_{\frac{\pi}{6}}^{\frac{\pi}{2}} \frac{r_2^2}{2} - \frac{r_1^2}{2} \, d\theta
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