Use an identity to write the expression as a single trigonometric function or as a single number.
-$\sin 22.5 ^ { \circ } \cos 22.5 ^ { \circ }$
A) $\frac { \sqrt { 3 } } { 3 }$

B) $\frac { \sqrt { 2 } } { 2 }$

C) $\frac { \sqrt { 2 } } { 4 }$

D) $\sqrt { 3 }$

Question

Use an identity to write the expression as a single trigonometric function or as a single number.
-$\sin 22.5 ^ { \circ } \cos 22.5 ^ { \circ }$
A) $\frac { \sqrt { 3 } } { 3 }$

B) $\frac { \sqrt { 2 } } { 2 }$

C) $\frac { \sqrt { 2 } } { 4 }$

D) $\sqrt { 3 }$

Quizplus · Accepted Answer

The expression can be simplified using the double angle formula for sine, which is $\sin(2\theta) = 2\sin(\theta)\cos(\theta)$. Here, $\theta = 22.5^\circ$, so $\sin(45^\circ) = 2\sin(22.5^\circ)\cos(22.5^\circ)$. Since $\sin(45^\circ) = \frac{\sqrt{2}}{2}$, the expression equals $\frac{\sqrt{2}}{2} = 2\sin(22.5^\circ)\cos(22.5^\circ)$, which simplifies to $\sin(22.5^\circ)\cos(22.5^\circ) = \frac{\sqrt{2}}{4}$.

Use an Identity to Write the Expression as a Single sin⁡22.5∘cos⁡22.5∘\sin 22.5 ^ { \circ } \cos 22.5 ^ { \circ }sin22.5∘cos22.5∘

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