Use the Half-Angle Formulas to Find the Exact Value of the Trigonometric

Multiple Choice

Use the Half-angle Formulas to find the exact value of the trigonometric function.
- $\sin 22.5 ^ { \circ }$

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