Find the exact value of the expression using the provided information.
-$\sin 25 ^ { \circ } \cos 35 ^ { \circ } + \cos 25 ^ { \circ } \sin 35 ^ { \circ }$
A) $\frac { \sqrt { 3 } } { 3 }$
B) $\frac { 5 } { 12 }$
C) $\frac { 1 } { 2 }$
D) $\frac { \sqrt { 3 } } { 2 }$

Question

Quizplus · Accepted Answer

This expression is an example of the sine addition formula, $\sin(a + b) = \sin a \cos b + \cos a \sin b$. Applying this formula with $a = 25^\circ$ and $b = 35^\circ$, we get $\sin(25^\circ + 35^\circ) = \sin(60^\circ)$, which equals $\frac{\sqrt{3}}{2}$.

Find the Exact Value of the Expression Using the Provided sin⁡25∘cos⁡35∘+cos⁡25∘sin⁡35∘\sin 25 ^ { \circ } \cos 35 ^ { \circ } + \cos 25 ^ { \circ } \sin 35 ^ { \circ }sin25∘cos35∘+cos25∘sin35∘

Find the Exact Value of the Expression Using the Provided $\sin 25 ^ { \circ } \cos 35 ^ { \circ } + \cos 25 ^ { \circ } \sin 35 ^ { \circ }$