Answer: B(t) = (0.03*Cos( pi*t/5) + 3.6) magnitudes.
Step-by-step explanation:
The question is not complete, but I will suppose that when t = 0, the brightness of the star is at the mean of 3.6 magnitudes.
Now, we know that the brightness oscillates with a period of 10 days and that the variation is equal to 0.3 magnitudes.
We know that the behavior is simple harmonic, so we can write this as:
B(t) = A*Cos(c*t) + K
Where A, c, and K are constants.
A defines the extreme values of the oscillation, so here we will have that A = 0.3 magnitudes.
K is the point around we have the oscillation, K is the average brightness of the star; K = 3.6 magnitudes.
c is a constant such the period is equal to 10 days.
We know that the period of the cosine function is equal to 2*pi
then we have: c*10 = 2pi
c = 2*pi/10 = pi/5
Then our equation is:
B(t) = (0.03*Cos( pi*t/5) + 3.6) magnitudes.
