The general cosine function is
a is the amplitude
b is a constant that determines the period, or is determined by the period
c is the (horizontal) phase shift
d is the vertical shift (centerline of the graph)
The given data is the following:
x (degrees) -60 -30 0 30 60 90 120
y 10 8 6 8 10 8 6
The function completes a cycle between (-60,10) and (60,10); 10 is the maximum value; 6 is the minimum value; 8 is the centerline value. That immediately tells us d=8 and a=2.
It also tells us that the period is 120 degrees; that means parameter b is 360/120 = 3.
Finally, the basic cosine function has its maximum value at x=0. The given function has a maximum values at x=60; so c is 60.
Now we have all the parameters we need to write the equation:
a = 2
b = 3
c = 60
d = 8
Here is a graph, showing constant functions at the minimum and maximum values and the center line....