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Trigonometry

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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.

A

$-\cfrac { \sqrt { 10 } }{ 3 }$

B

$-\cfrac { 3\sqrt { 10 } }{ 10 }$

C

$\sqrt{10}$

D

$\cfrac { \sqrt { 10 } }{ 3 }$

E

$-\sqrt{10}$