I know that the sine function in the domain $[0,1)$ is surjective, I know that since I was a child, in these days I'm thinking how to prove it formally.
Anyone can help me with this?
I know that the sine function in the domain $[0,1)$ is surjective, I know that since I was a child, in these days I'm thinking how to prove it formally.
Anyone can help me with this?
With the geometric definition of sine: For $0
Otherwise (i.e without geometrical reference), the surjectivity is a consequence of the sine function being continuous together with $\sin 0 = 0$ and $\sin\frac\pi2=1$.