Solve the Problem $\sin \frac { \theta } { 2 }$

Multiple Choice

Solve the problem.
-Find $\sin \frac { \theta } { 2 }$ , given that $\cos \theta = \frac { 1 } { 4 }$ and $\theta$ terminates in $0 < \theta < 90 ^ { \circ }$ .

A) $\frac { \sqrt { 8 + 2 \sqrt { 15 } } } { 4 }$

B) $\frac { \sqrt { 6 } } { 4 }$

C) $\frac { \sqrt { 8 - 2 \sqrt { 15 } } } { 4 }$

D) $\frac { \sqrt { 10 } } { 4 }$