study of sunspots. spots in a year min. is 10, max is 110. between max's of 1750 & 1948, 18 cycles occurred. Find a sinusoidal equation to model this.

Question

My equation looks something like this so far:

y=50sin(2pi/11(x-d))+60

so How do I get the phase shift? d? I am confused about what would be x and y to plug into the formula and find d? Because the max occurs at 1750, but what would be the x and y values to sub in and why?

Answer 1

y=50sin( 2pi(x-d)/11 )+60
when x = 1750, you have a max and sin (2 pi(1750-d)/11) = 1
or 2 pi (1750-d)/11 = pi/2 (90 degrees for max of sin function)
1750-d =11/4 (in other words a quarter of a cycle after start)
d = 1750 - 11/4

Answer 2

How did you get 1750-d=11/4?

Answer 3

I mean, so would d = 1747.25
ie
y=50sin(2pi/11(x-1747.25))+60