If , where and denotes the greatest integer function,…

MATHEMATICS · Single correct · AoPS · Mathematics · Special Functions · Special Functions

Problem

[\sin x]+[\sqrt{2}\cos x]=-3

, where

x\in[0,2\pi]

and

[\cdot]

denotes the greatest integer function, then (1)

x\in\left(\pi,\frac{5\pi}{4}\right)

(2)

x\in\left(\pi,\frac{7\pi}{6}\right)

(3)

x\in\left[\pi,\frac{5\pi}{4}\right]

(4) None of these