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Trigonometry

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Moderate

Rotated Sine for $(5,4)$

TRIG-4S2EKG

The line segment from the origin containing the point $(5,4)$ is rotated about the origin $-\pi$ radians.

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

A

$-\cfrac { 4\sqrt { 41 } }{ 41 }$

B

$\cfrac { 4\sqrt { 41 } }{ 41 }$

C

$-\cfrac { 5\sqrt { 41 } }{ 41 } $

D

$\cfrac { 5\sqrt { 41 } }{ 41 }$

E

$-\cfrac { \sqrt{ 41 } }{ 4 }$