Use The Half-Angle Formulas
-$\sin 15 ^ { \circ }$
A) $\frac { 1 } { 2 } \sqrt { 2 - \sqrt { 3 } }$
B) $\frac { 1 } { 2 } \sqrt { 2 + \sqrt { 3 } }$
C) $- \frac { 1 } { 2 } \sqrt { 2 + \sqrt { 3 } }$
D) $- \frac { 1 } { 2 } \sqrt { 2 - \sqrt { 3 } }$

Question

Quizplus · Accepted Answer

The half-angle formula for sine is $\sin \frac{\theta}{2} = \pm \sqrt{\frac{1 - \cos \theta}{2}}$. For $\theta = 30^\circ$, $\cos 30^\circ = \frac{\sqrt{3}}{2}$, so $\sin 15^\circ = \sqrt{\frac{1 - \frac{\sqrt{3}}{2}}{2}} = \frac{1}{2} \sqrt{2 - \sqrt{3}}$.

Use the Half-Angle Formulas - sin⁡15∘\sin 15 ^ { \circ }sin15∘

Use the Half-Angle Formulas
- $\sin 15 ^ { \circ }$