Use an identity to write the expression as a single trigonometric function or as a single number.
-$\sin 22.5 ^ { \circ }$
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) $\frac { 1 } { 2 } \sqrt { 2 + \sqrt { 2 } }$

Question

Quizplus · Accepted Answer

$\sin 22.5^\circ$ can be found using the half-angle formula: $\sin \frac{\theta}{2} = \pm \sqrt{\frac{1 - \cos \theta}{2}}$. For $\theta = 45^\circ$, $\cos 45^\circ = \frac{\sqrt{2}}{2}$, so $\sin 22.5^\circ = \sqrt{\frac{1 - \frac{\sqrt{2}}{2}}{2}} = \frac{1}{2}\sqrt{2 - \sqrt{2}}$.

Use an Identity to Write the Expression as a Single sin⁡22.5∘\sin 22.5 ^ { \circ }sin22.5∘

Use an Identity to Write the Expression as a Single $\sin 22.5 ^ { \circ }$