Video Example 2 b D 0 100 Sketch the curve r 1 sin 0 Solution Instead of plotting points we first sketch the graph of r 1 sin 0

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Video Example 2 b D 0 100 Sketch the curve r 1 sin 0 Solution Instead of plotting points we first sketch the graph of r 1 sin 0 in Cartesian coordinates in the top figure by shifting the sine curve up one unit This enables us to read at a glance the values of r that correspond to increasing values of 0 For instance we see that as so we sketch the corresponding part of the polar curve in figure a As 0 increases from to the top figure shows that r decreases from 3 2 0 increases from 0 to r the distance from O increases from to to so we sketch the 2 as shown in part d If we let 0 increase beyond 2n or decrease 3r as shown in part c Finally as 0 increases from r decreases from to 2n r increases from next part of the curve as in figure b As increases from it to 2 beyond 0 we would simply retrace our path Putting together the parts of the curve from figures a d we sketch the complete curve in part e It is called a cardioid because it s shaped like a heart 2 2 n 0 to to

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