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Trigonometry

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Quadruple Angle Cosecant Given Sine

TRIG-J1W4FR

If angle $\theta$ has a sine of $\cfrac{\sqrt{5}}{4}$, and $\theta$ lies in Quadrant II, determine the cosecant for angle $4\theta$.

A

$-\cfrac{\sqrt{55}}{8}$

B

$-\cfrac{32\sqrt{55}}{165}$

C

$-\cfrac{4\sqrt{55}}{155}$

D

$-\cfrac{16\sqrt{11}}{11}$

E

$\cfrac{16\sqrt{11}}{11}$