A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

vera_ewing

  • one year ago

Math question

  • This Question is Closed
  1. vera_ewing
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

  2. Michele_Laino
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    since: \[ - 1 \leqslant \cos \left( {4x + \pi } \right) \leqslant 1\] then we can write: \[3 \leqslant - 3\cos \left( {4x + \pi } \right) + 6 \leqslant 9\] so the requested amplitude is \[A = \frac{{9 - 3}}{2} = 3\]

  3. Michele_Laino
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    for period T, we can write this: \[\begin{gathered} \cos \left( {4x + \pi } \right) = \cos \left( {4x} \right)\cos \pi - \sin \left( {4x} \right)\sin \pi = \hfill \\ \hfill \\ = - \cos \left( {4x} \right) \hfill \\ \end{gathered} \] so our function becomes: \[f\left( x \right) = 3\cos \left( {4x} \right) + 6\]

  4. Michele_Laino
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    now, if we make this change of variable: \[y = 4x\] then our function becomes: \[f\left( y \right) = 3\cos \left( y \right) + 6\] As you can know, the period of that function is \[T = 2\pi \] So what can you conclude?

  5. Michele_Laino
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    oops..as you well know...

  6. Michele_Laino
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    @vera_ewing

  7. Michele_Laino
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    the amplitude of a periodic function, has to be always positive

  8. Michele_Laino
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    since the cos(x) function is such that: -1 </ cos(x) </ 1, here </ stands for "less or equal to" then we can write: 3</ f(x) </ 9 so the amplitude is: A=(9-3)/2=...?

  9. Michele_Laino
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    furthermore, if we make this change of variable: 4x=y, then we can rewrite your fuunction as follows: f(x)=3*cos(4x)+6, and therefore: f(y) = 3 cos(y)+6 the period of that function is T= 2*pi, so what can you conclude?

  10. Michele_Laino
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I'm sorry, I can not give the direct answer, since I have to respect the Code of Conduct

  11. Michele_Laino
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I think that option D is a wrong answer!

  12. Michele_Laino
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    the period can not be 2*pi, since as I wrote before, if we use this substitution: y=4x then your function as a function of y has period = 2*pi, whereas as function of x has the period equal to: (2*pi)/4=...?

  13. vera_ewing
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    1.57

  14. Michele_Laino
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    better is pi/2

  15. Michele_Laino
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    now using the same substitution, we have these correspondences: x--->y/4 and therefore: pi---> pi/4 so what can you conclude about the phase shift?

  16. vera_ewing
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    The phase shift is x=pi/4 ?

  17. Michele_Laino
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    the phase shift is a relative quantity, so we can assume taht it is - pi/4

  18. Michele_Laino
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    that*

  19. vera_ewing
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Oh so the answer is A!

  20. Michele_Laino
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yes!

  21. vera_ewing
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Michele thank you so much! :)

  22. Michele_Laino
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    :)

  23. 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.