# Trigo is not such easy!!

Algebra Level 5

If $$\lfloor 2 \cos x \rfloor + \lfloor \sin x \rfloor =-3$$ for $$x \in [0, 2 \pi]$$, then the range of the function $$f(x)= \sin x+\sqrt 3 \cos x$$ can be written as $$[a, b]$$. Find $$a^2 + b^2$$.



Notation: $$\lfloor \cdot \rfloor$$ denotes the floor function.

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