Modeling with sinusoidal functions

Given the description of a real-world relationship, find the sinusoidal function that models it.

Problem

Aditya's dog routinely eats Aditya's leftovers, which vary seasonally. As a result, his weight fluctuates throughout the year.
The dog's weight W, left parenthesis, t, right parenthesis (in k, g) as a function of time t (in days) over the course of a year can be modeled by a sinusoidal expression of the form a, dot, cosine, left parenthesis, b, dot, t, right parenthesis, plus, d.
At t, equals, 0, the start of the year, he is at his maximum weight of 9, point, 1, space, k, g. One-quarter of the year later, when t, equals, 91, point, 25, he is at his average weight of 8, point, 2, space, k, g.
Find W, left parenthesis, t, right parenthesis.