Confusion over a trigronometric function

Question

I found 2 solutions

But they say it is:

It feels like there's a mistake in the shift here, I tested it on Desmos and the functions doesn't reflect the perihelion and aphelion years. Do you guys have a different understanding of the shift here? Thanks :)

Answer 1

You're confused because you are looking at the wrong section of the graph. Your $t$ is the time before/after the year 2000. So, your horizontal axis should be set to something like $(-50, 150)$, rather than something like $(1950,2150)$.

So, their answer is correct.