Graphs of Polar equations

Like most other types of equations, there are many graph shapes that fall under the category of polar equations. The simplest of these are the line through the orgin or just a normal circle. Others that fall under this category are spirals, cardioids, lemniscates, limacons, and rose curves. An element that all do these graphs have in common is the use of theta, with the exception of the circle at the orgin. While the appearance of circles, lines, and spirals may seem obvious, the other four are a little more complex. Cardioids are essentially heart-shaped graphs that go up and down for sin and left and right for cos. Limacons are graphs with either an interior loop, a climpled side, or just convex, depending on the value of a/b. Rose curves are basically graphs that look like flowers. Their number of pedals is dependent on the value of n. Lemniscates look like an infinity sign, and are either on the x-axis for cos or diagonal for sin.