# Thread: problem with polar coordinates

1. ## 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.

2. Originally Posted by dylan5188
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.
$\displaystyle r_1 = \sqrt{1 + \frac{1}{3}} = \frac{2}{\sqrt{3}}$

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

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

$\displaystyle \theta_2 = \frac{\pi}{2}$

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