Exercise 1.3.28

Question

A variable star is one whose brightness alternately increases and decreases. For the most visible variable star, Delta Cephei, the time between periods of maximum brightness is 5.4 days, the average brightness (or magnitude) of the star is 4.0, and its brightness varies by $\pm$0.35 magnitude. Find a function that models the brightness of Delta Cephei as a function of time.

Khagan Gulusoy · Accepted Answer

Since the brightness of the star varies by $\pm$0.35, the amplitude (the factor by which we have to stretch the cosine curve vertically) is equal to 0.35. Since the time between periods of maximum brightness is 5.4 days and the period of the cosine function is equal to $2\pi,$ the horizontal stretching factor is $\dfrac{2\pi}{5.4}$. Since the average brightness of Delta Cephei is equal to $4.0,$ the shifting upward factor is $4.0.$ That way, the brightness function is modeled as follows:
$$\forall t\in [0,+\infty):\quad b(t)=4+0.35\cos\left(\frac{2}{5.4}\pi\cdot x\right).$$

Exercise 1.3.28

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Exercise 1.3.28

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