Hey there! Sign in to join this conversationNew here? Join for free
    • Thread Starter
    Offline

    0
    ReputationRep:
    im a bit confused on how to work out each of the the letters stated in the equation could someone please help me?

    y = z+ a * sin(bx + c)

    z=average value
    a=amplitude
    b=angular frequency
    c=Phase angle

    Im very lost on how to work out these letters from a given graph which is usually sin or cos graph...anyone help?
    Offline

    15
    ReputationRep:
    z will be where the horizontal centre line of the graph lies.

    a is by how much the curve deviates from this line.

    b is how squashed/stretched the graph is as a scale factor. (eg. sin2x is a wave of half the length of sinx)

    c is how much the graph has been shifted by from the origin.
    • Thread Starter
    Offline

    0
    ReputationRep:
    how would you work them out?
    Offline

    15
    ReputationRep:
    Exactly as I said, you require the graph to work them out properly.
    Offline

    15
    ReputationRep:
    If you want me to be really detailed then:

    z is the value of y at which the sine wave is split in half.

    a is given by |(max value of the sine wave) - z|

    b is given by the distance from the start to finish of a single oscillation and comparing to 2pi.

    c is given by how far from the origin the (0,0) point on a normal sine wave has been shifted in the x-direction. By convention |c|< pi.
    • Thread Starter
    Offline

    0
    ReputationRep:
    how would u go about doin this question?

    A function f (x) is known to be of the form y = z+ a * sin(bx + c) where all the constants are non-negative. It has a local maximum at (pi,6) and the next local minimum is
    at (5pi, –1). Find the formula for the function.
    Offline

    15
    ReputationRep:
    First, draw a sine wave with no axes. Then put points for that maximum and the next minimum.

    z is given by the mean in the y-values =7/2

    a is given by the max height - z = 5/2

    b is given by the comparison in wavelength = 1/2

    c is given by the shift (first maximum usually occurs at (pi/2,1) in a normal sine wave) = pi/2.
    • Thread Starter
    Offline

    0
    ReputationRep:
    (Original post by marcusmerehay)
    First, draw a sine wave with no axes. Then put points for that maximum and the next minimum.

    z is given by the mean in the y-values =7/2

    a is given by the max height - z = 5/2

    b is given by the comparison in wavelength = 1/2

    c is given by the shift (first maximum usually occurs at (pi/2,1) in a normal sine wave) = pi/2.
    what about for the cos graph?
    Offline

    15
    ReputationRep:
    (Original post by mathslover786)
    what about for the cos graph?
    A cos graph works in exactly the same way, as it's just a translation of a sine graph.

    cos(x + pi/2) = sin(x)

    The only difference in working from the example I did for you would be that the first maximum on a cos graph occurs at (0,1).
    • Thread Starter
    Offline

    0
    ReputationRep:
    (Original post by marcusmerehay)
    A cos graph works in exactly the same way, as it's just a translation of a sine graph.

    cos(x + pi/2) = sin(x)

    The only difference in working from the example I did for you would be that the first maximum on a cos graph occurs at (0,1).
    ah ok cheers
 
 
 
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • Poll
    Would you rather give up salt or pepper?
    Useful resources

    Make your revision easier

    Maths

    Maths Forum posting guidelines

    Not sure where to post? Read the updated guidelines here

    Equations

    How to use LaTex

    Writing equations the easy way

    Student revising

    Study habits of A* students

    Top tips from students who have already aced their exams

    Study Planner

    Create your own Study Planner

    Never miss a deadline again

    Polling station sign

    Thinking about a maths degree?

    Chat with other maths applicants

    Can you help? Study help unanswered threads

    Groups associated with this forum:

    View associated groups
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

    Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

    Write a reply...
    Reply
    Hide
    Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.