Find the Exact Value of the Composition $\cos \left( \sin ^ { - 1 } \left( \frac { 1 } { 4 } \right) \right)$

Multiple Choice

Find the exact value of the composition.
- $\cos \left( \sin ^ { - 1 } \left( \frac { 1 } { 4 } \right) \right)$

A) $\frac { \sqrt { 15 } } { 2 }$
B) $\frac { 2 \sqrt { 15 } } { 15 }$
C) $\frac { \sqrt { 15 } } { 4 }$
D) $\frac { 4 \sqrt { 15 } } { 15 }$