Rewrite the Following as a Product of Trigonometric Functions $\sin ( \mathrm { s } - \mathrm { t } )$

Multiple Choice

Rewrite the following as a product of trigonometric functions.
-Find $\sin ( \mathrm { s } - \mathrm { t } )$ given that $\cos \mathrm { s } = \frac { 1 } { 3 }$ , with $\mathrm { s }$ in quadrant $\mathrm { I }$ , and $\sin \mathrm { t } = \frac { 1 } { 4 }$ , with $\mathrm { t }$ in quadrant II.

A) $\frac { - 12 \sqrt { 30 } - 1 } { 2 }$
B) $\frac { - 30 \sqrt { 2 } - 1 } { 12 }$
C) $\frac { - 2 \sqrt { 30 } - 1 } { 12 }$
D) $\frac { - 12 \sqrt { 2 } - 1 } { 30 }$