Use the appropriate addition formula to find the exact value of the expression.
-$\cos \left( \frac { 19 \pi } { 12 } \right)$
A) $- \sqrt { 6 } - \sqrt { 2 }$
B) $\frac { \sqrt { 2 } - \sqrt { 6 } } { 4 }$
C) $\sqrt { 2 } - \sqrt { 6 }$
D) $\frac { \sqrt { 6 } - \sqrt { 2 } } { 4 }$

Question

Quizplus · Accepted Answer

The expression $\cos \left( \frac { 19 \pi } { 12 } \right)$ can be rewritten using the addition formula for cosine as $\cos \left( \frac { 16 \pi } { 12 } + \frac { 3 \pi } { 12 } \right) = \cos \left( \frac { 4 \pi } { 3 } \right) \cos \left( \frac { \pi } { 4 } \right) - \sin \left( \frac { 4 \pi } { 3 } \right) \sin \left( \frac { \pi } { 4 } \right)$. Evaluating each term gives $\frac { \sqrt { 6 } - \sqrt { 2 } } { 4 }$.

Use the Appropriate Addition Formula to Find the Exact Value cos⁡(19π12)\cos \left( \frac { 19 \pi } { 12 } \right)cos(1219π​)

Use the Appropriate Addition Formula to Find the Exact Value $\cos \left( \frac { 19 \pi } { 12 } \right)$