Moderate# Rotated Cosecant for $(3,9)$

TRIG-TEEXWG

The line segment from the origin containing the point $(3,9)$ is rotated about the origin $-\cfrac { \pi }{ 2 }$ radians.

Determine the cosecant of the new angle formed between the line segment from the origin that contains the new coordinate and the positive $x$-axis.