In our section on transformation of graphs, we have explained that, given the graph y = f(x),the following indicate scaling is necessary.

                                       g(x) = a f(x)

                                             g(x) = f(ax)

Here we will explain this idea with relation to trigonometric graphs.

 

This page will deal with scaling along the y-axis.

 

Take the example y = 2 sin x

 

                                   

 

From the graph, it is noticed that the amplitude of the graph is now 2. The period of the graph has not changed.

 

Now look at the graph of y = 0.5 sin x

 

                                 

The amplitude is now changed to 0.5. The period, like the above curve, remains the same.

 

In general, in the case of y-scaling, for the sine and cosine curves, given the graph of the form y = a sin x or y = a cos x, the amplitude of the graph is a. For the tangent and reciprocal functions, the (magnitude of) gradient of the graphs increase.

 

 

The next page deals with x-scaling.