Intuition behind the horizontal factor in a sinusoidal function

Question

I came across the following question:

And here is an excerpt of its solution:

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I understand how the horizontal factor is calculated:

$period=\frac{2\pi}{horizontal factor}$

$365=\frac{2\pi}{horizontal factor}$

$horizontal factor = \frac{2\pi}{365}$

However, I don't understand its implication for/how it connects to the scenario described in the question.