1.1.6 Transforming the Parameter (Circles)
Next I want to explore the effect on the image curve of transforming the parameter. Formally this means we are changing a parent function into the function for constants and .
We'll begin by analyzing the unit circle. Back in PreCal you learned to parameterize the unit circle via:
In this class I'll refer to this as the standard parameterization of the unit circle.
In the applet below, experiment by changing the values of and to see the effect on the image curve. Jot down your observations.
Eliminate the parameter in the standard parameterization of the unit circle to obtain a rectangular equation for the image curve. How does transforming the parameter affect this rectangular equation?