How do you graph $y = 2 cos 5 x$ $y=2cos5x$ ?

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How do you graph $y = 2 cos 5 x$ $y=2cos5x$ ?

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Answer 1 · 2016-10-28T19:46:01

Graph a cosine function with an amplitude of $2$ $2$ and a period of $\frac{2 π}{5}$ $(2pi)/5$ .

Explanation:

Graph $y = 2 cos 5 x$ $y=2cos5x$ .

This equation is in the form $y = A cos B x$ $y=AcosBx$ where

$A =$ $A=$ amplitude and $\frac{2 π}{B} =$ $(2pi)/B=$ 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 $y = cos x$ $y=cosx$ .. It has an amplitude of $1$ $1$ and a period of $2 π$ $2pi$ .

desmos

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

demos

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

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How do you graph $y = 2 cos 5 x$ $y=2cos5x$ ?

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