A Cepheid variable star is a star whose brightness alternately increases and decreases. For a certain star, the interval between times of maximum brightness is 5.7 days. The average brightness of this star is 3.0 and its brightness changes by ±0.55. Using this information, the brightness of the star at time t, where t is measured in days, has been modeled by the function B(t) = 3.0 + 0.55 sin (2). (a) Find the rate of change of the brightness at time t days. dB dt (b) Find the rate of change of brightness at time t = 1 day. dB dt

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