Video Example Sketch the curve r 1 sin 0 A 3 m 2 b 2

Last updated: 4/15/2023

Video Example Sketch the curve r 1 sin 0 A 3 m 2 b 2 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 T see that as increases from 0 to r the distance from O increases from so we sketch the corresponding part 2 of the polar curve in figure a As increases from to the top figure shows that r decreases from 2 c 1 d 3 sketch the next part of the curve as in figure b As increases from to r decreases from 2 e 8 37 c Finally as increases from to 27 r increases from as shown in part d If we let increase beyond 27 or 2 decrease 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 a 8 T 8 EIN 210 0 14 0 0 0 5 18 2 A 0 0 377 De 8 2T 0 377 to to to to so we as shown in part