Use the Formula for the Cosine of the Difference of Two Angles
-$\cos \left( 255 ^ { \circ } - 15 ^ { \circ } \right)$
A) $- \frac { 1 } { 2 }$
B) $- \frac { \sqrt { 3 } } { 2 }$
C) $\frac { 17 } { 4 }$
D) $\frac { \sqrt { 3 } } { 2 }$

Question

Quizplus · Accepted Answer

The formula for the cosine of the difference of two angles is $\cos(\alpha - \beta) = \cos \alpha \cos \beta + \sin \alpha \sin \beta$. Applying this to $\cos(255^\circ - 15^\circ) = \cos(240^\circ)$, and knowing that $\cos(240^\circ) = -\frac{1}{2}$, we find the correct answer.