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1. Area bounded by polar sec and csc curves ●○○○○ 10 ptsFind the area of the region bounded by the graph of $r = \sec \theta$, the graph of $r = \csc \theta$, the $x$-axis, and the $y$-axis.
2. Area of a polar sector ●○○○○ 10 ptsFind the area of the region given in polar coordinates by $\frac{\pi}{4}\leq\theta \leq\frac{\pi}{2}$ and $0\leq r\leq 2$, using a double integral. Round to two decimal places.
3. Area of a triangle in polar coordinates ●○○○○ 10 ptsIn the polar coordinate system, points $A\left(2, \frac{\pi}{6}\right)$ and $B\left(4, \frac{\pi}{3}\right)$ are given, and $O$ is the pole. Find the area $S$ of $\triangle AOB$.
4. Area enclosed by a lemniscate ●●○○○ 20 ptsUse a double integral in polar coordinates to find the area of the region enclosed by the lemniscate $r^2=4\cos(2\theta)$. Include both lobes.
5. Area swept by a rotating cardioid ●●●○○ 50 ptsThe polar curve $r = 1 + \cos \theta$ is rotated once around the point with polar coordinates $(2,0)$. What is the area of the region it sweeps over? Round to two decimal places.