Use a sum or difference identity to find the exact value.
-$\sin 185 ^ { \circ } \cos 65 ^ { \circ } - \cos 185 ^ { \circ } \sin 65 ^ { \circ }$
A) $- \frac { \sqrt { 3 } } { 2 }$
B) $\frac { \sqrt { 3 } } { 2 }$
C) $- \frac { 37 } { 12 }$
D) $- \frac { 1 } { 2 }$

Question

Quizplus · Accepted Answer

Using the sum identity for sine, we have:$\sin 185 ^ { \circ } \cos 65 ^ { \circ } - \cos 185 ^ { \circ } \sin 65 ^ { \circ }$$= \sin (185 ^ { \circ } + 65 ^ { \circ })$$= \sin 250 ^ { \circ }$$= \sin (360 ^ { \circ } - 110 ^ { \circ })$$= \sin 110 ^ { \circ }$$= \frac { \sqrt { 3 } } { 2 }$

Use a Sum or Difference Identity to Find the Exact sin⁡185∘cos⁡65∘−cos⁡185∘sin⁡65∘\sin 185 ^ { \circ } \cos 65 ^ { \circ } - \cos 185 ^ { \circ } \sin 65 ^ { \circ }sin185∘cos65∘−cos185∘sin65∘

Use a Sum or Difference Identity to Find the Exact $\sin 185 ^ { \circ } \cos 65 ^ { \circ } - \cos 185 ^ { \circ } \sin 65 ^ { \circ }$