Use Sum and Difference Formulas for Cosines and Sines
-$\sin 260 ^ { \circ } \cos 20 ^ { \circ } - \cos 260 ^ { \circ } \sin 20 ^ { \circ }$
A) $- \frac { \sqrt { 3 } } { 2 }$
B) $- \frac { 1 } { 2 }$
C) $\frac { 13 } { 3 }$
D) $\frac { \sqrt { 3 } } { 2 }$

Question

Quizplus · Accepted Answer

This expression can be simplified using the sine difference formula: $\sin(A - B) = \sin A \cos B - \cos A \sin B$. Applying this formula, we get $\sin(260^\circ - 20^\circ) = \sin(240^\circ)$. The sine of 240 degrees, which is in the third quadrant where sine is negative, equals $-\frac{\sqrt{3}}{2}$.

Use Sum and Difference Formulas for Cosines and Sines - sin⁡260∘cos⁡20∘−cos⁡260∘sin⁡20∘\sin 260 ^ { \circ } \cos 20 ^ { \circ } - \cos 260 ^ { \circ } \sin 20 ^ { \circ }sin260∘cos20∘−cos260∘sin20∘

Use Sum and Difference Formulas for Cosines and Sines
- $\sin 260 ^ { \circ } \cos 20 ^ { \circ } - \cos 260 ^ { \circ } \sin 20 ^ { \circ }$