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Trigonometry

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Moderate

Rotated Cosecant for $(-2,3)$

TRIG-XTDH4B

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

A

$\cfrac { \sqrt { 13 } }{ 2 }$

B

$\cfrac { 2\sqrt { 13 } }{ 13 }$

C

$-\cfrac { \sqrt { 13 } }{ 3 } $

D

$\cfrac { \sqrt { 13 } }{ 3 }$

E

$-\cfrac { 3\sqrt { 13 } }{ 13 }$