I'm trying to figure out what am I doing wrong in these calculations.
I need to graph $0.6 = 2.5\sin(2\pi ft)$ where $f = 1000 Hz$.
In order to find half of a period I solve $2\pi f = k\pi$ from which I get $t = \frac{k}{2f}$. I have the first three zeros (where the sine is zero) at $t_0 = 0, t_1 = 0.0005, t_2 = 0.001$ seconds. I've confirmed this in Desmos.
However, now when I try to see where the $2.5\sin(2\pi f)$ expression intercepts the 0.6 line, I do:
$$0.6 = 2.5\sin(2\pi ft) \iff t = \frac{\arcsin(\frac{0.6}{2.5})}{2\pi f} = \frac{13.885654}{6283.185307} = 0.00221$$
Well, this makes no sense at all since half of a period is $0.0005$ and I should have at least 2 solution between $t_0$ and $t_1$. In Wolfram I get for these solutions $t_0^* = 0.0000385737$ and $t_1^* = 0.000461426$, which obviously make more since since both are smaller than the period.
What am I thinking wrong and how can I get the Wolfram result?