# How do you graph and list the amplitude, period, phase shift for y=cos(2x)?

Jun 4, 2018

Below

#### Explanation:

$y = \cos \left(2 x\right)$
This equation can be placed in the general form: $y = a \cos \left(n x + c\right)$ where a is the amplitude, n can be used to find the period and c tells you whether you shift the equation left or right

From $y = \cos \left(2 x\right)$
We can tell immediately that the amplitude is 1 ie $a = 1$
The Period is found by $T = \frac{2 \pi}{n}$ where n is the coefficient of the x ie $T = \frac{2 \pi}{n} = \frac{2 \pi}{2} = \pi$secs

Since $c = 0$, there is no phase shift

Now all you have to do is to graph your equation. What the period tells you is how long it takes to finish one cycle. So if the period is pi, then you draw the ENTIRE cos graph from $0 \le x \le 2 \pi$ within $0 \le x \le \pi$

For example below is $y = \cos x$ ---- (1)
ie graph{cosx [-10, 10, -5, 5]}

Now check out $y = \cos \left(2 x\right)$ ---- (2)

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

You will hopefully notice that the two cosine graphs are found in the (2) than (1)

And now check out $y = \cos \left(3 x\right)$

graph{cos(3x) [-10, 10, -5, 5]}

You will notice that there are 3