A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • one year ago

Can someone help me with determining the equation for a trig function? I'm aware of how to find the amplitude and period, i'm just confused with this graph!

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

  2. MTALHAHASSAN2
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    wait how can we find the amplitute

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

    it's usually the "a", I know how to determine it by looking at an equation

  4. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\large \text{amplitude} = \frac{|m-n|}{2}\] m = largest y coordinate of a point on the curve n = smallest y coordinate of a point on the curve

  5. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1444532222391:dw|

  6. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1444532254763:dw|

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

    in this case it would be 2+4/2

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

    which would be 3..

  9. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yes

  10. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    the midline is found by averaging the two extreme values \[\Large D = \frac{m+n}{2}\] y = D is the equation of the midline |dw:1444532397834:dw|

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

    the midline is -1

  12. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1444532428898:dw|

  13. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    `the midline is -1` yes

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

    so for the period since the points aren't actually on the radians how would I calculate where it starts and where it ends?

  15. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    look at the peak that lies on the y axis this is when x = 0 the next peak over to the right is at x = pi so the period is |pi - 0| = |pi| = pi units

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

    I'm a little confused..

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

    when x=0 y=2, is that the peak that you're talking about?

  18. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    see the attached image

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

    ok thanks! I got that. I'm just confused why we are subtracting the pi-0. I thought the formula for period was 2pi/k

  20. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    you might be thinking of T = 2pi/B and that is useful when you have an equation of this form y = A*cos(Bx - C) + D

  21. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I subtracted the x values to find the distance between them

  22. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    the absolute value is to ensure the distance is positive

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

    so for this graph we don't need to use that form. We just find distance simply by finding out the x values from the y and subtract them from one another?

  24. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    you can pick on any 2 neighboring peaks and do the same thing

  25. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    we can't use that form because we don't have the equation

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

    oh ok! That's where I was confused at :)

  27. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    you might have learned how to pick apart y = A*cos(Bx - C) + D (eg find the amplitude to be |A|, etc) but now we're going in reverse: finding the key elements and using them to construct the equation

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

    so our equation would be y=3sin(x)-1?

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

    y=sin(pi)-1

  30. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    what is y when x = 0 ?

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

    2

  32. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    but does plugging in x = 0 give y = 2 when you use y = 3*sin(x) - 1 ?

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

    no

  34. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    so that equation doesn't fit

  35. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    let's try cos instead of sin

  36. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    if x = 0, does y = 2 for y = 3*cos(x) - 1 ?

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

    it does fit

  38. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yep, ok how about if x = pi/2, does y = -4 like it should?

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

    we know that cos(x)=1

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

    I don't think so

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

    cos of pi/2 is 1

  42. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    cos(pi/2) = 0 actually

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

    and 3-1=2, and 2-1=1

  44. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    recall that the period is pi units so T = pi Solve the equation T = 2pi/B for B to get... T = 2pi/B pi = 2pi/B B*pi = 2pi B = 2pi/pi B = 2 so the equation should be y = 3*cos(2x) - 1

  45. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    now if we try x = pi/2, then y = 3*cos(2x) - 1 y = 3*cos(2*pi/2) - 1 y = 3*cos(pi) - 1 y = 3*(-1) - 1 y = -3 - 1 y = -4 and it fits

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

    I'm a little lost. Why are we using t=2pi/3?

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

    B*

  48. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    The period is T = pi going from peak to peak is pi units across

  49. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    plug T = pi into T = 2pi/B and solve for B to get B = 2

  50. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    T = 2pi/B is the period formula If you know B, you can find the period T (or vice versa)

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

    so we just knew the T, but in order to find b we had to plug in pi for t

  52. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    exactly

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

    and how did you know that y=-4?

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

    just the point on the graph?

  55. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    1 Attachment
  56. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Yes the point (pi/2, -4) is on the graph Notice how in my work above I replaced x with pi/2 in the equation y = 3*cos(2x) - 1 Then I evaluated/simplified to get y = -4. So that confirms the equation works for x = pi/2

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

    oh so you just replaced it to check to see if the equation that we wrote was correct.. makes sense. :) Thank you lots!

  58. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yes I recommend you check x = pi as well. Make sure that the output is y = 2

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

    Thanks again :) You're a life saver! I honestly had a lot of trouble with this problem

  60. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I'm glad it's making sense now

  61. 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.