If only graph paper were elastic...

One of the troubles trig students sometimes have deals with the amplitude and frequency of a trig graph. One approach I stressed was to recognize that the basic shape of the sine curve, for example, never changed. Just its position.

This is more evident when we look at the sine curves on an elastic graph paper.

In this example, drag the coefficient sliders to new values. You will see that the graph paper stretches or shrinks in each direction so that the graph stays put.

Neat, isn't it?