Find a restricted domain so that the function is injective The sinus function is not injective when the domain is the whole $\mathbb{R}$. 
To find a restricted domain where the function is injective, can we do that only using the graph or is there also an other way? 
Such a resticted domain is for example $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right ]$. How can we find it? 

Find the interval on the graph is fine.
As an alternative we can consider the trigonometric circle and choose any angular interval such that any value for $\sin \theta $ is reached exactly one time.
The more natural choice is $\theta\in \left[-\frac \pi 2, \frac \pi 2\right]$ but there are many other possibilities of course as for example


*

*$\theta\in \left[\frac \pi 2, 3\frac \pi 2\right]$

*$\theta\in \left[3\frac \pi 2, 5\frac \pi 2\right]$
and more in general all the intervals
$$[\theta_1,\theta_2]\subseteq  \left[-\frac \pi 2+k\pi, \frac \pi 2+k\pi\right]$$
works fine.
