Polar Graphing w/ Cartensian connection
- Tom Ahlschwede
How to use this Sketch
Here is the graph of a cartesian function of the form y = a + b*sin(cx). There are sliders for a, b, and c. THEN, look up. There is the polar version that corresponds to r = a + b*sin(c*theta). There is a point on the cartesian graph, "MoveThisPt," drag it around and see how the x and y point translates to the r and theta point. Note places of 0, pi, pi/2, 2pi, etc. In the sliders, if a is set to zero, then the polar graph is a rose. If C is even the number of petals is doubled, if C is odd that is the number of petals. Then, if you set C to 1 and then make a non-zero, then you have the family of cardioids. There are predominantly three forms, a = b, a < b, and a < b. Enjoy.