Find the exact value of the expression.
-$\sin 25 ^ { \circ } \cos 95 ^ { \circ } + \cos 25 ^ { \circ } \sin 95 ^ { \circ }$
A) $- \frac { 1 } { 2 }$
B) $\frac { 1 } { 6 }$
C) $- \frac { \sqrt { 3 } } { 2 }$
D) $\frac { \sqrt { 3 } } { 2 }$

Question

Quizplus · Accepted Answer

This expression is an application of the sine addition formula, $\sin(a + b) = \sin a \cos b + \cos a \sin b$. Here, $a = 25^\circ$ and $b = 95^\circ$, so the expression simplifies to $\sin(25^\circ + 95^\circ) = \sin(120^\circ)$. The sine of 120 degrees, which is in the second quadrant where sine values are positive, is $\frac{\sqrt{3}}{2}$.

Find the Exact Value of the Expression sin⁡25∘cos⁡95∘+cos⁡25∘sin⁡95∘\sin 25 ^ { \circ } \cos 95 ^ { \circ } + \cos 25 ^ { \circ } \sin 95 ^ { \circ }sin25∘cos95∘+cos25∘sin95∘

Find the Exact Value of the Expression $\sin 25 ^ { \circ } \cos 95 ^ { \circ } + \cos 25 ^ { \circ } \sin 95 ^ { \circ }$