How do you graph y=-1-3cos4x?

1 Answer
Jun 15, 2018

Know how the cosine curve behaves and some standard values of it.

Explanation:

First off, rearanging terms gives, y=-3cos4x-1.

This means you will have a negative cosine curve, and because of the -1 the curves center will be moved down by 1.

Also notice how for all x, cos(x) is between -1,1, and because cosx is multiplied by 3 in y it will now oscillate between -3,3.

We now know the center and its max/min value. Now for the shape.

Start with plugging in values into y that will give us known values for cosine which is:
cos(0)=1,
cos(\pi/2)=0,
cos(\pi)=-1,
cos({3\pi}/2)=0,
cos(2\pi)=1.
(These values can easily be seen in the unitcircle where cosine is the x value.)

We do only need these values to know how the curve will look for all x as cosine is periodic and will repeat forever. This will also apply to the negative side as cosine is an even function (cos(-x)=cos(x)).

So we want to insert som x into y such that we get these known values. Lets start off with getting cos(0)=1 in y.

4x=0=>y(0)=-4
4x=\pi/2=>y(\pi/8)=-1
4x=\pi=>y(\pi/4)=2
4x={3\pi}/2=>y({3\pi}/8)=-1
4x=2\pi=>y(\pi/2)=-4

Now insert these (x,y) pairs into a cordinate system and connect the dots! Note, as its the negative cosine we want to plot, the function will start by increasing from x=0 instead of decreasing.