ITMC 2018 Grade 11 National Preliminary set01 Question 16

Real $x\in[0,2\pi]$ satisfies $\sin(x-4)=-1$. How many statements are correct? (1) $\sin x\lt 0$; (2) $\cos x\gt 0$; (3) $\sin2x\gt 0$; (4) $\cos2x\lt 0$.