Simple question about circles.

Question

Let's say I have a set $S=\{(x,y): x^2+y^2=1\}$. I want to prove that for every $i \in [-1,1]$ there's a point $(i,y) \in S$.

I know this sounds pretty trivial, but I need this fact for a another proof and I don't know how to prove this.

Answer 1

For $i\in [-1,1]$, we have $1-i^2 \ge 0$. Let $y = \pm \sqrt{1-i^2}$.

Answer 2

If $i \in [-1,1]$ then $$ (i,\sin(\mathrm{arcos}(i))). $$