A variable star is one whose brightness alternately increases and decreases. For one such star, the time between periods of maximum brightness is 5.6 days, the average brightness (or magnitude) of the star is 5.5, and its brightness varies by ±0.30 magnitude. Find a 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 5.5 and that it is increasing.)

Answer 1

since we have our minimum at t=0, the function will look like

y = -cos(kt)

The brightness varies by ±0.30, so that is the amplitude.

y = -0.30 cos(kt)

Since the low is 5.5, the axis of the curve is at 5.5+0.30, so

y = 5.80 - 0.30cos(kt)

The period of cos(kt) is 2π/k, so we must have

2π/k = 5.6, or k = π/2.8

y = 5.80 - 0.30cos(π/2.8 t)