anonymous
  • anonymous
What is the amplitude, period, and phase shift of y= 5cos( x/2 + 2pi/3) ?????
Mathematics
schrodinger
  • schrodinger
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shadowfiend
  • 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?
shadowfiend
  • 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.
anonymous
  • anonymous
\[y= 5\cos (1/2(x + 4\pi/3)) ???\]

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shadowfiend
  • 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?
anonymous
  • anonymous
So amplitude is 5, period is 4pi, and phase shift is 4pi/3 ?
shadowfiend
  • shadowfiend
You got the amplitude and period, just adjust the phase shift to the fix I made to the equation.
anonymous
  • anonymous
I thought you have to push the 1/2 out of the parentheses to get the proper phase shift?
shadowfiend
  • shadowfiend
Whoops, yes, good call, sorry, brain fart. So you nailed it :D
shadowfiend
  • shadowfiend
Boom! Nice one :)
anonymous
  • 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
anonymous
  • anonymous
Ok, for starters, the phase shift is 4pi/3 to the RIGHT.....right? Trying to graph this

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