Prove that the following function is bijective and calculate its inverse
$$f : [0, \frac{\pi}{2}] \to \mathbb R, \qquad f(x)= x - \cos (x)$$
Proved it's injective (increasing on $2k\pi < x < \frac{3\pi}{2}+2k\pi$, where k is a constant in Z, which is included in $[0, \frac{\pi}{2}]$ ) but I'm not sure to prove it's surjective
I calculated the limits for $-\infty$ and $\infty$ but the results aren't in the co-domain. I'm pretty sure I'm missing something but don't know what. Any ideas ?