[Math] The exact value of csc -420 degrees (Find the exact value of each trigonometric funtion)

trigonometry

I'am very confused, I have looked all over google and I can not find out how too do this problem.
I have the answer its number 14 since our teacher gives us the answer but we need to show work.enter image description here

I understood number 13 it was $\sec -210^\circ$, but I can't figure out how too do #14. How can it be $-2 \sqrt{3}/ 3$? I just can't figure this problem out.

Any help would be greatly appreciated. The problem is $\csc -420^\circ$.

Best Answer

$$\csc(-420^\circ)=-\csc 420^\circ=-\csc 60^\circ=-\frac{2\sqrt3}{2}$$