Hi! The solution to this question may be completely trivial, but I still managed to get stuck on this equation. So I wish to solve:

$\displaystyle a \cos(x) + b \sin(x) = 1$

for $\displaystyle x$. Hence, I want to express $\displaystyle x$ as a function of $\displaystyle a$ and $\displaystyle b$. And for which values of $\displaystyle a$ and $\displaystyle b$ does there exist a solution?