Determine the Exact Value Of $\csc \theta$ When $\cos \theta = \frac { 11 } { 61 }$

Determine the exact value of $\csc \theta$ when $\cos \theta = \frac { 11 } { 61 }$ and $\sin \theta < 0$ .

A) $\csc \theta = - \frac { 1 } { 60 }$

B) $\csc \theta = - \frac { 61 } { 60 }$

C) $\csc \theta = - \frac { 60 } { 61 }$

D) $\csc \theta = - \frac { 61 } { 30 }$

E) $\csc \theta = - \frac { 62 } { 59 }$