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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