# Sketching a polar curve

Continued off the question I asked earlier, I also have to sketch the curve.

$r^2=−4\sin(2\theta)$

So I have to set up a table of values I'm assuming. How do I know what values to choose for $\theta$. Then I'm just lost all together trying to plot the theta and $r$ values to get the curve.

Oh and one quick other question. If it also asks me to find all the points of intersections and to set up the integral to evaluate the area inside after sketching the curve, what does that mean? Do I have to pick a top and bottom or something? Confused about that.

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To get started, you might try values of $\theta$ where it's easy to calculate stuff, like $\theta=0,\pi/12,\pi/4,\pi/2,\dots$. Maybe even better to note first that since $r^2\ge0$ it only makes sense to take $\theta$ with $\sin2\theta\le0$.