A Cepheid variable star is a star whose brightness alternately increases and decreases. Suppose that Cephei Joe is a star for which the interval between times of maximum brightness is 4.6 days. Its average brightness is 3.7 and the brightness changes by +/-0.25. Using this data, we can construct a mathematical model for the brightness of Cephei Joe at time $t$, where $t$ is measured in days: $$B(t) = 3.7 + 0.25\sin(2 \pi t/4.6)$$ (a) Find the rate of change of the brightness after $t$ days.
Rate of change =

(b) Find the rate of increase after one day.
Rate of increase =