Anonymous
posted by trig .
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.
My equation looks something like this so far:
y=50sin(2pi/11(xd))+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?

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

I mean, so would d = 1747.25
ie
y=50sin(2pi/11(x1747.25))+60