The cosecant function is the reciprocal of the sine function.
So if you think about the ratios of a triangle for sine, you have opposite/hypotenuse.
For cosecant, it will be hypotenuse/opposite.
Placing the angle on the xy axes
225° is 45° past 180°.
The hypotenuse for a unit circle is positive 1. And the opposite side is negative and a value of -1/√2
So you want to calculate 1/(-1/√2) = -√2