Determine All Solutions of the Equation in Radians $\cos ( s + t )$

Multiple Choice

Determine all solutions of the equation in radians.
-Find $\cos ( s + t )$ given that $\sin s = - \frac { 1 } { 2 }$ , with $s$ in quadrant IV, and $\sin t = \frac { 1 } { 4 }$ , with $t$ in quadrant II.

A) $- \frac { 4 \sqrt { 3 } + \sqrt { 15 } } { 11 }$
B) $\frac { 1 + 3 \sqrt { 5 } } { 8 }$
C) $\frac { 4 \sqrt { 3 } - \sqrt { 15 } } { 11 }$
D) $\frac { 1 - 3 \sqrt { 5 } } { 8 }$