A Cepheid variable star is a star whose brightness alternately increases and decreases. The most easily visible such star is Delta Cephei, for which the interval between times of maxi - mum brightness is 5.4 days. The average brightness of this star is 4.0 and its brightness changes by ± 0.35. In view of these data, the brightness of Delta Cephei at time t, where t is measured in days, has been modeled by the function
B(t) = 4.0 + 0.35 sin (2πt/5.4)
(a) Find the rate of change of the brightness after days.
(b) Find, correct to two decimal places, the rate of increase after one day.