Use Identities to Fill in the Blank with the Appropriate $\sin ( \mathrm { s } - \mathrm { t } )$

Multiple Choice

Use identities to fill in the blank with the appropriate trigonometric function name.
-Find $\sin ( \mathrm { s } - \mathrm { t } )$ given that $\sin \mathrm { s } = - \frac { 1 } { 2 }$ , with $\mathrm { s }$ in quadrant $\mathrm { IV }$ , and $\sin \mathrm { t } = \frac { 1 } { 4 }$ , with $\mathrm { t }$ in quadrant II.

A) $\frac { \sqrt { 15 } + \sqrt { 3 } } { 8 }$
B) $\frac { - \sqrt { 15 } - \sqrt { 3 } } { 8 }$
C) $\frac { - \sqrt { 15 } + \sqrt { 3 } } { 8 }$
D) $\frac { \sqrt { 15 } - \sqrt { 3 } } { 8 }$