This is an excerpt from my textbook:
Find the argument and expression in polar coordinates for (a) $z=3i$ and (b) $w=-\sqrt3+i$
(a) $|-3i| = |-3||i| = 3$, so, in polar coordinates, $-3i = 3(\cos\theta +i\sin\theta)$, and thus $\cos\theta=0$ and $\sin\theta=-1$. This yields that $\arg(-3i)=\theta=\frac{3\pi}2+2\pi k,\;k\in\mathbb Z$ Thus, in polar coordinates, $-3i = 3e^{i3\pi/2}$
(b) $|-\sqrt3+i| = \sqrt{3+1} = 2$, so in polar coordinates, $-\sqrt3+i=2(\cos\theta+i\sin\theta)$, thus $\cos\theta = -\frac{sqrt3}2$ and $\sin\theta=\frac12$. Therefore, $\arg(-\sqrt3+i)=\theta=\frac{5\pi}6+2\pi k,\;k\in\mathbb Z$. Thus, in polar coordinates, $-\sqrt3+i=2e^{i5\pi/6}$
What I do not understand is quite simple I think: how does he go from $\cos\theta=0$ and $\sin\theta=-1$ to $\arg(-3i)=\frac{3\pi}2 +2\pi k$ And please explain it for the second part also. I just dont seem to understand the unit circle properly.