Question

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

Answer 1

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?

Answer 2

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

Answer 3

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

Answer 4

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?

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

Boom! Nice one :)

Answer 10

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

Answer 11

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