Find the Exact Value of the Expression Using the Provided $\sin ( s - t )$

Find the exact value of the expression using the provided information.
-Find $\sin ( s - t )$ given that $\cos s = \frac { 1 } { 3 }$ , with $s$ in quadrant $\mathrm { I }$ , and $\sin t = \frac { 1 } { 4 }$ , with $\mathrm { t }$ in quadrant II.

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

Correct Answer:

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