Strange results for solving boundary angle of full reflection

157 Views Asked by At

I was trying to solve the following group of equations for $\alpha$ using Wolfram|Alpha:

$$\frac{v_2\cdot\sin(\alpha)}{v_1} = 1 \\ v_1 > 0 \\ v_2 > 0$$

I expected something like $\alpha = \sin^{-1}(\frac{v_1}{v_2})$ but instead got: $$v_1 > 0\text{ and }v_2>0\text{ and }\alpha = 2 \pi n-\sin^{-1}\left(\frac{v_1}{v_2}\right)+\pi\text{ and }n \in \mathbb{Z}$$

Can someone explain why Wolframp|Alpha gives this answer?