a is the amplitude.
b is the frequency.
c is the horizontal shift.
d is the vertical shift.
in your equation, you have:
a = 2
b = 3
c = 0
d = -2
since a = 2, your graph will go from y = 2 to y = -2 because the amplitude is plus or minus from the center line of the graph and the center line of the graph is y = 0 unless there is a vertical displacement.
since the vertical displacement is -2, the center line of you graph will shift down 2 units from 0 to -2 and your amplitude rance becomes y = 2 to -2.
since b = 3, your frequency is 3 times the normmal frequency of a sine wave.
this means that the period of each full sine wave will be 1/3 * the period of a normal sine wave whose frequency is 1.
the normal sine wave has a period of 360 degrees if you are working in degrees, or 2 * pi if you are working in radians.
period = 360 / frequency if you are dealing in degrees.
period = 2 * pi / frequency if you are dealing in radians.
since your frequency is 3, your period becomes:
360 / 3 = 120 degrees if you are dealing in degrees.
2 * pi / 3 = 2pi/3 if you are dealing in radians.
the easy way to draw the graph is to use graphing software.
the hard way is to manually plot selected points and then draw the curve between them.
i'll take the easy way and show you what the graphs will look like when you are using degrees and when you are using radians.
the first picture below shows you what the graph would look like if you are using degrees.
the second picture below shows you what the graph would look like if you are using radians.
you convert from degrees to radians by multiplying degrees by pi / 180.
you convert from radians to degrees by multiplying radians by 180 / pi.
