Two different angles whose amplitudes are in the interval $[0,2\pi]$ have the same sine. What is the sum of their amplitudes?
A. $\pi$ $$\\$$ B. A multiple of $\pi$ $$\\$$ C. A multiple of $2\pi$ $$\\$$ D. $2\pi$
I know that the amplitudes of these angles have to be $\alpha$ and $\pi-\alpha$ and so
$$(\pi-\alpha)+\alpha = \pi$$
But my book says the solution is B. I can't understand how that is though, as I couldn't seem to find any 2 diferent anges of amplitude within the given interval for which the sum would be a multiple of $\pi$.
Can someone explain this to me?