If $y = a\sin{x} + b\cos{x} +C$ then find maxima and minima for $y$. I was able to solve it till
$$y = \sqrt{(a^2 + b^2)}\sin(\alpha + x)  +  C.$$
But I don't know how to find maxima and minima from here.
If $C = 0$ then maxima & minima equals the amplitude of the sine curve but when $C$ is non-zero then?
I need help from here onwards.

Hint:

*

*$\sin(\alpha +x) \in [-1,1]$
$$ \therefore \quad \sqrt{a^2+b^2}\sin(\alpha+x) \in \left[ - \sqrt{a^2+b^2}, \sqrt{a^2+b^2} \right]$$
$$ \quad \therefore \sqrt{a^2+b^2}\sin(\alpha+x)+C \in \left[C- \sqrt{a^2+b^2}, C+ \sqrt{a^2+b^2}\ \right] \quad ,$$ therefore the maximum of $y$ is $_____$, and the minimum of $y$ is $_____$.
