What's the biggest subset of $R$ for which $\sin(x)$ is injective?

Question

My guess is $[-\pi/2,\pi/2]$, although there are many others of this size for which $\sin x$ would be injective, but I'm not sure...

Answer 1

You are right in that this is the biggest subset, and that there are many (in fact infinitely many) subsets of the same size. You could generalise the answer for $n$ where $n$ is an integer.

e.g.

$R=\Big[\frac{(n-1)\pi}{2},\frac{n\pi}{2}\Big], \forall n \in \mathbb{N}$