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# Sine wave equation watch

1. 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?
2. 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.
3. how would you work them out?
4. Exactly as I said, you require the graph to work them out properly.
5. 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.
6. 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.
7. 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.
8. (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?
9. (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).
10. (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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