A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

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
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    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
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    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
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  4. shadowfiend
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    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
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  6. shadowfiend
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  7. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  8. shadowfiend
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  9. shadowfiend
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Boom! Nice one :)

  10. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    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
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  12. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.