Michael’s weight fluctuates according to a sinusoidal function of time. Let x = 0 correspond to the beginning of the year (January, 1st). Because of his new year resolutions, Michael loses weight and reaches a minimum of 205 pounds at x = 60 days. Michael then stops exercising and dieting and his weight increases to a maximum of 250 pounds at x = 140 days.Here is what I got:

If summer starts on the day x = 171 and ends on the day x = 265, how many days of summer will Michael’s weight be below 220 pounds (these are the days he fits into his bathing suit)?

Using the sinusoidal function Asin((2pi/B)(x-C))+D

I got22.5sin((2pi/160)(x-100))+227.5

So where do I go after I go the equation?

ALSO, another curious question (if anyone got time or wants to answer it), how do you get rid of a sin in an equation.

Thanks!