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

1 Answer
Sep 21, 2015

Answer:

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

Explanation:

You have: #y=1/2 cos(4x)#

Well, the easiest way is to start from the known function #cos(x)#
which can be drawn as such:
graph{cos x [-10, 10, -5, 5]}

The cosine function is 1 at #x=0#.
The cosine function is 0 at #x=pi/2#.

That is, our function will be 0 when the inner term of the cosine function reaches #pi/2#.
But we have #(4x)# inside our cosine.
So this means that our cosine function reaches 0
when #4x=pi/2#
or after rearranging, when
#x=pi/8# (and #-pi/8# and so on).

The following is the graph of #cos(4x)#:
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 #cos(0.5x)# would expand the cosine wave along the x-axis.)

Finally, we have an external multiplicative factor of #1/2#, which compresses the "height" of our cosine wave (along the y-axis this time) in half.
graph{(1/2)cos (4x) [-10, 10, -5, 5]}

That's it. Hope this helps.