## A community for students. Sign up today

Here's the question you clicked on:

## anonymous 5 years ago What is the amplitude, period, and phase shift of y= 5cos( x/2 + 2pi/3) ?????

• This Question is Closed
1. shadowfiend

There's a pretty straightforward way to identify those: $y = a \cos \left( bx + c \right)$ In that equation, $$a$$ is the amplitude, $$b$$ is the period, and $$c$$ is the phase shift. Can you rewrite your equation in that form?

2. shadowfiend

To be clear, b is not the period exactly. $$\frac{2\pi}{b}$$ is the period. Sorry, I didn't make that obvious above.

3. anonymous

$y= 5\cos (1/2(x + 4\pi/3)) ???$

4. shadowfiend

Close, there's no need to pull the 1/2 out of the entire thing though :) You can just pull it out of the x part: $y = 5 \cos \left(\frac{1}{2}x + \frac{2\pi}{3}\right)$ So then what are a, b, and c?

5. anonymous

So amplitude is 5, period is 4pi, and phase shift is 4pi/3 ?

6. shadowfiend

You got the amplitude and period, just adjust the phase shift to the fix I made to the equation.

7. anonymous

I thought you have to push the 1/2 out of the parentheses to get the proper phase shift?

8. shadowfiend

Whoops, yes, good call, sorry, brain fart. So you nailed it :D

9. shadowfiend

Boom! Nice one :)

10. anonymous

Thanks! Do you happen to know how I can find "the appropriate interval on which to graph one complete period of the function f" ? I am TERRIBLE at finding the graphs for these

11. anonymous

Ok, for starters, the phase shift is 4pi/3 to the RIGHT.....right? Trying to graph this

#### Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy