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# Rotated Cosecant for $(4,-6)$

TRIG-D41XGT

The line segment from the origin containing the point $(4,-6)$ is rotated about the origin $-\cfrac {3 \pi }{ 4 }$ radians. Determine the cosecant 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

$5.099$

B

$5.100$

C

$-5.099$

D

$-1.171$

E

$1.020$