I have been studying Trigonometric Functions and I'm having a bit of a hard time understanding on how to solve for the phase shift (C) is y=asin(bx+c)+d.
Here is my understanding so far: a = amplitude
b = period - which is usually 2pi/b
c = phase shift
d = vertical shift.
So I can solve for a,b,d but I am unable to determine how we can figure out what the phase shift is. I've gone through many websites in vain but none really explain how we can solve for the value of phase shift (C).
Take this for example. I need to develop a function that graphs hours of rain fall a day in a fake country for 365. (Extreme Fake Scenario)
Using my Coordinates which are (x,y) x being the days and y being the hours of rainfall.
Instead of plotting hours of rain every single day for 365 days, I have chosen to do every 15 days and logged the hours of rain like that. From using this information, I was then able to use videos and websites to help me develop this formula
2.75sin (2pi/365 (x)- C) + D
I have gotten this far, but I am unable to solve for C. The only thing I found that really helped was doing pi/2 which allowed the function to fit the curve perfectly. Can someone please help me through this. I have made a graph of my points which can be found here: https://www.desmos.com/calculator/goecrf783f