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    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?
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    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.
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    how would you work them out?
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    Exactly as I said, you require the graph to work them out properly.
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    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.
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    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.
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    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.
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    (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?
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    (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).
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    (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
 
 
 
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