Single Variable Calculus, Chapter 1, 1.3, Section 1.3, Problem 26

The brightness of a variable star alternately increases and decreases.
Delta Cephei, the most visible variable star, has maximum brightness between period of 5.4 days.
The average brightness 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.



The graph of sine function is best suited for the values that alternately increases and decreases.
Recall that the full period of a sine funciton is $2 \pi$ so we obtain the equation...

$
\begin{equation}
\begin{aligned}
Y &= A \sin(2 \pi ft) \quad \text{ or can be written as }\\
Y &= A \sin\left(\displaystyle \frac{2\pi}{T}t\right)
\\
\\
\text{where: } A &= \text{amplitude of the sine wave }\\
f&= \text{frequency }\\
T&= \text{period }\\
t&= \text{time}
\end{aligned}
\end{equation}
$




Plugging all the given data to the general equation of sine we obtain...

$f(t)= 4\pm 0.35 \sin \displaystyle \left(\frac{2\pi}{5.4}t\right)$