a is the amplitude
b is the frequency
c is the horizontal displacement
d is the vertical displacement.
i translated your equation to use the same terminology.
it becomes y = 2 * cos(4 * (x - pi/6)) + 12
the amplitude is 2 so the cosine will bo from +2 to -2 of the center line.
the center line is 12.
the curve will be shifted 30 degrees to the right, so the high amplitude of the curve would be at pi/6 rather than at 0.
the frequency is 4.
this means you will get 4 full cycles in the interval that would normally be 1 full cycle.
the formula to use is frequendcy = 2 * pi / period and period = 2 * pi / frequency.
you are looking for the period so the formula would be 2 * pi / 4 = pi/2 which means you should get a full cycle of the cosine wave form every pi/2 radians or every 90 degrees.
the formula for translating radians to degrees is degrees = radians * 180 / pi.
the formula for translating degrees to radians is radians = degrees * pi / 180.
here's the graph.
the black dots are showing you the full cycle marks.
they are at 0, pi/2, pi, 3pi/2 and 2pi.
you can see that the cosine wave is shifted to the right by about 30 degrees.
because the graph is repetitive, this is now always too easy to see.
here's a reference on the general form of the sine wave.
