Use a sum or difference identity to find the exact value.
-$\sin 10 ^ { \circ } \cos 110 ^ { \circ } + \cos 10 ^ { \circ } \sin 110 ^ { \circ }$
A) $\frac { \sqrt { 3 } } { 2 }$
B) $- \frac { \sqrt { 3 } } { 2 }$
C) $- \frac { 1 } { 2 }$
D) $\frac { 1 } { 6 }$

Question

Quizplus · Accepted Answer

The sum identity for sine is $\sin(a+b)=\sin(a)\cos(b)+\cos(a)\sin(b)$. So, $\sin 10 ^ { \circ } \cos 110 ^ { \circ } + \cos 10 ^ { \circ } \sin 110 ^ { \circ } = \sin (10 ^ { \circ } + 110 ^ { \circ }) = \sin 120 ^ { \circ } = \frac { \sqrt { 3 } } { 2 }$.

Use a Sum or Difference Identity to Find the Exact sin⁡10∘cos⁡110∘+cos⁡10∘sin⁡110∘\sin 10 ^ { \circ } \cos 110 ^ { \circ } + \cos 10 ^ { \circ } \sin 110 ^ { \circ }sin10∘cos110∘+cos10∘sin110∘

Use a Sum or Difference Identity to Find the Exact $\sin 10 ^ { \circ } \cos 110 ^ { \circ } + \cos 10 ^ { \circ } \sin 110 ^ { \circ }$