Find the exact value of the expression.
-$\sin 15 ^ { \circ }$
A) $- \frac { \sqrt { 2 } ( \sqrt { 3 } - 1 ) } { 4 }$

B) $\frac { \sqrt { 2 } ( \sqrt { 3 } + 1 ) } { 4 }$

C) $\frac { \sqrt { 2 } ( \sqrt { 3 } - 1 ) } { 4 }$

D) $- \frac { \sqrt { 2 } ( \sqrt { 3 } + 1 ) } { 4 }$

Question

Find the exact value of the expression.
-$\sin 15 ^ { \circ }$
A) $- \frac { \sqrt { 2 } ( \sqrt { 3 } - 1 ) } { 4 }$

B) $\frac { \sqrt { 2 } ( \sqrt { 3 } + 1 ) } { 4 }$

C) $\frac { \sqrt { 2 } ( \sqrt { 3 } - 1 ) } { 4 }$

D) $- \frac { \sqrt { 2 } ( \sqrt { 3 } + 1 ) } { 4 }$

Quizplus · Accepted Answer

The exact value of $\sin 15^\circ$ can be found using the half-angle formula: $\sin \frac{\theta}{2} = \sqrt{\frac{1 - \cos \theta}{2}}$. For $\sin 15^\circ$, we use $\theta = 30^\circ$, so $\sin 15^\circ = \sqrt{\frac{1 - \cos 30^\circ}{2}} = \sqrt{\frac{1 - \sqrt{3}/2}{2}} = \frac{\sqrt{2}(\sqrt{3} - 1)}{4}$.

Find the Exact Value of the Expression sin⁡15∘\sin 15 ^ { \circ }sin15∘

Find the Exact Value of the Expression $\sin 15 ^ { \circ }$