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

Question

Quizplus · Accepted Answer

The exact value of $\cos \left( \frac { 19 \pi } { 12 } \right)$ can be found by expressing it as a sum or difference of angles for which the cosine values are known. $\frac { 19 \pi } { 12 }$ can be rewritten as $\frac { 16\pi } { 12 } + \frac { 3\pi } { 12 } = \frac { 4\pi } { 3 } + \frac { \pi } { 4 }$. Using the cosine sum formula, $\cos(a + b) = \cos(a)\cos(b) - \sin(a)\sin(b)$, and knowing the exact values for $\cos(\frac { 4\pi } { 3 }) = -\frac { 1 } { 2 }$ and $\cos(\frac { \pi } { 4 }) = \frac { \sqrt { 2 } } { 2 }$, $\sin(\frac { 4\pi } { 3 }) = -\frac { \sqrt { 3 } } { 2 }$, and $\sin(\frac { \pi } { 4 }) = \frac { \sqrt { 2 } } { 2 }$, the calculation yields $\frac { \sqrt { 6 } - \sqrt { 2 } } { 4 }$.

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

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