Answer: csc -675 = √2
Explanation:
Keep adding 360 to find your reference angle.
-675 + 360 = -315
-315 + 360 = 45
Your reference angle is 45°
csc 45 =

Remember your unit circle:
sin 45 =

Substitute:
csc 45 =
>Keep change flip
csc 45 = 2/√2 >Get rid of root on bottom
csc 45 =

csc 45 = √2
csc -675 = √2