The general sine function is
a is the amplitude
b determines or is determined by the period
c is the horizontal phase shift
d is the vertical shift (determines the center line)
Here are the data:
-120 -60 0 60 120 180 240
1.5 3 1.5 0 1.5 3 1.5
The values oscillate between 0 and 3 over an interval of 240 degrees. That immediately tells us...
d is 1.5 (the graph oscillates about the middle value of 1.5)
a is 1.5 (the values oscillate 1.5 either side of the middle value)
the period is 240 degrees; that means b is 360/240 = 3/2 or 1.5
The "start point" for the basic sine graph is when the function value is the center value and increasing. For this function, the function value is the center value of 1.5 and increasing at 120 degrees, so the phase shift c is 120.
We have all the parameters we need to write the equation:
Here is a graph, showing the sine function along with the constants representing the center line and minimum and maximum values.