I have to find the constants $k_1$ and $k_2$ of the function $g(y)=k_1 \cos (\sqrt{\alpha}y)+k_2 \sin (\sqrt{\alpha}y) $ in using $g(0)=g(b)=0$. So I found that $k_1=0$. Furthermore, I think $\alpha = (\frac{n \pi}{b})^2$, $n \in \mathbb{Z}$, but I don't know which value $k_2$ have to take.
Silly question : Is anyone could tell me the value of $k_2$ and why?