# How do you graph and list the amplitude, period, phase shift for #y=3cos4x#?

##### 1 Answer

The cosine function's general form is

and the basic form we all know and love has

If we focus on functions with

Hence A adjusts the amplitude of the cosine function.

Now, lets look at what k does.

If we were to put

More generally, we get

as we increase k to some value

Finally, lets look at the phase constant.

Lets say

So, lets look at our function:

We can see that

We know that it will start where we expect since there is no phase shift. The amplitude is now 3, so the graph will be stretched in the y direction - ranging from

graph{3cos(4x) [-2.7, 13.32, -3.57, 4.44]}

As you can see from the graph, this is true. The amplitude is 3 and there are 4 wavelengths between 0 and