Use a Sum or Difference Identity to Find the Exact $\sin ( \mathrm { s } - \mathrm { t } )$

Use a sum or difference identity to find the exact value.
-Find $\sin ( \mathrm { s } - \mathrm { t } )$ given that $\cos \mathrm { s } = \frac { 1 } { 3 }$ , with $\mathrm { s }$ in quadrant $\mathrm { I }$ , and $\sin t = - \frac { 1 } { 2 }$ , with $\mathrm { t }$ in quadrant IV.

A) $\frac { \sqrt { 3 } - 2 \sqrt { 2 } } { 6 }$
B) $\frac { 2 \sqrt { 6 } + 1 } { 6 }$
C) $\frac { \sqrt { 3 } + 2 \sqrt { 2 } } { 6 }$
D) $\frac { 2 \sqrt { 6 } - 1 } { 6 }$