Let $\alpha$ be an angle, with $0\leq \alpha < 2\pi$. Given $\cos(2\alpha)=\frac{31}{49}$ and $3\pi/2<2\alpha<2\pi$, find exact values of the six trigonometric functions.
Note: You are not allowed to use decimals in your answer.

$\sin(\alpha)$ = .

$\cos(\alpha)$ = .

$\tan(\alpha)$ = .

$\csc(\alpha)$ = .

$\sec(\alpha)$ = .

$\cot(\alpha)$ = .