How do you graph # y=2cos5x#?

1 Answer
Shell
Oct 28, 2016

Graph a cosine function with an amplitude of #2# and a period of #(2pi)/5#.

Explanation:

Graph #y=2cos5x#.

This equation is in the form #y=AcosBx# where

#A=#amplitude and #(2pi)/B=# the period.

Amplitude is the distance on the y-axis between the center line of the graph and the "peak" or "trough".

Period is the distance on the x-axis of one full "cycle" or "repeat" of the graph.

Let's start with #y=cosx#.. It has an amplitude of #1# and a period of #2pi#.

desmos

Next, let's graph #y=2cosx#. Notice the amplitude has doubled from #1# on the red graph to #2# on the blue graph.

demos

Last, let's look at #y=2cos5x# in green. The period is #(2pi)/5#.
In other words, one complete "cycle" of cosine is graphed between zero and #(2pi)/5#.
desmos

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