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The line segment from the origin containing the point $(5,-8)$ is rotated about the origin $\cfrac { \pi }{ 6 }$ radians. Determine the secant 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

$1.887$

B

$28.577$

C

$1.132$

D

$1.133$

E

$0.530$

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