A variable star is one whose brightness alternately increases and decreases, which can be modeled using a sine function. For one such star, the time between periods of maximum brightness is 5.1 days, the average brightness of the star is 5.4, and its brightness varies by 0.30 (so the difference between maximum brightness and minimum brightness is 0.6). Find a sine function that models the brightness of the star as a function of time (in days), t. Assume that at t = 0 the brightness of the star is 5.4 and that it is increasing.

f(t) =