# How do you graph #y = 1/2cos( 4x )#?

##### 1 Answer

See explanation, graph{(1/2)cos (4x) [-10, 10, -5, 5]}

#### Explanation:

You have:

Well, the easiest way is to start from the known function

which can be drawn as such:

graph{cos x [-10, 10, -5, 5]}

The cosine function is 1 at

The cosine function is 0 at

That is, our function will be 0 when the inner term of the cosine function reaches

But we have

So this means that our cosine function reaches 0

when

or after rearranging, when

The following is the graph of

graph{cos (4x) [-10, 10, -5, 5]}

The factor "4" actually compresses the cosine wave along the x-axis.

(Note: if the factor were between 0 and 1, say, for example, 0.5, then

Finally, we have an external multiplicative factor of

graph{(1/2)cos (4x) [-10, 10, -5, 5]}

That's it. Hope this helps.