The number of sunspots (solar storms on the sun) fluctuates with roughly 11-year cycles with a high of 120 and a low of 0 sunspots detected. A peak of 120 sunspots was detected in the year 2000.

Question

what is the trigonometric functions could be used to approximate this cycle?

Answer 1

starting with the peak at t=0 suggests use of a cosine function. Since the period is 11 years, start with

y = cos(2π/11 t)

The amplitude is (120-0)/2 = 60, so

y = 60 cos(2π/11 t)

The center line is at y=60, so

y = 60 cos(2π/11 t) + 60

where t is the number of years since 2000.