We see a collection of polar curves.
1 Lines
1.1 Horizontal lines
\[ \graph [polar]{a=1,r=a \csc (\theta )} \]
1.2 Vertical lines
\[ \graph [polar]{a=1,r=a \sec (\theta )} \]
1.3 Not through the origin
\[ \graph [polar]{b=1,m=1,r=\frac {b}{\sin (\theta )-m \cos (\theta )}} \]
2 Circles
2.1 Centered on the x-axis
\[ \graph [polar]{a=1, r=a \cos (\theta )} \]
2.2 Centered on the y-axis
\[ \graph [polar]{a=1,r=a \sin (\theta )} \]
2.3 Centered at the origin
\[ \graph [polar]{a=1,r=a} \]
3 Archimedean spiral
\[ \graph [polar]{r=\theta } \]
4 Limaçons
4.1 With inner loop
\[ \graph [xmin=-5,xmax=5,ymin=-2,ymax=2,polar]{a=1,b=2,r=a+b \cos (\theta )} \]
\[ \graph [xmin=-5,xmax=5,ymin=-.5,ymax=3.5,polar]{a=1,b=2,r=a+b \sin (\theta )} \]
4.2 Cardioid
\[ \graph [xmin=-5,xmax=5,ymin=-2,ymax=2,polar]{a=1,b=a,r=a+b \cos (\theta )} \]
\[ \graph [xmin=-5,xmax=5,ymin=-1,ymax=2.5,polar]{a=1,b=a,r=a+b \sin (\theta )} \]
4.3 Dimpled
\[ \graph [polar]{a=3,b=2,r=a+b \cos (\theta )} \]
\[ \graph [xmin=-10,xmax=10,ymin=-2,ymax=6,polar]{a=3,b=2,r=a+b \sin (\theta )} \]
4.4 Convex
\[ \graph [xmin=-20,xmax=20,ymin=-7.5,ymax=7.5,polar]{a=5,b=2,r=a+b \cos (\theta )} \]
\[ \graph [xmin=-20,xmax=20,ymin=-5.5,ymax=10,polar]{a=5,b=2,r=a+b \sin (\theta )} \]
5 Rose curves
\[ \graph [xmin=-5,xmax=5,ymin=-2,ymax=2,polar]{r=\cos (2\theta )} \]
\[ \graph [xmin=-5,xmax=5,ymin=-2,ymax=2,polar]{r=\sin (2\theta )} \]
\[ \graph [xmin=-5,xmax=5,ymin=-2,ymax=2,polar]{r=\cos (3\theta )} \]
\[ \graph [xmin=-5,xmax=5,ymin=-2,ymax=2,polar]{r=\sin (3\theta )} \]
2025-01-06 20:20:34