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Rotated Cotangent for $(5,9)$

TRIG-PYNFXT

The line segment from the origin containing the point $(5,9)$ is rotated about the origin $-\cfrac {2 \pi }{ 3 }$ radians.

Determine the cotangent to three decimal places of the new angle formed between the line segment from the origin that contains the new coordinate and the positive $x$-axis.

A

$0.600$

B

$-0.599$

C

$0.604$

D

$-0.600$

E

$60.600$