Video Example 2 Sketch the curve r 1 + sin(0). Solution 0 2 N 0 increases from 0 to to to to so we sketch the as shown in part (d). If we let 0 increase beyond 2 or decrease 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 r (the distance from O) increases from , so we sketch the corresponding part of the polar curve in figure (a). As 0 increases from to n, the top figure shows that r decreases from as shown in part (c). Finally, as 0 increases from 3 to 2, r increases from ,r decreases from next part of the curve as in figure (b). As 0 increases from ir to 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 cardiold because it's shaped like a heart. (a) 3t 2 to (b) 2 7110 0-0 @