Use the appropriate addition formula to find the exact value of the expression.
-$\sin \left( \frac { 17 \pi } { 12 } \right)$
A) $- \frac { \sqrt { 6 } + \sqrt { 2 } } { 4 }$
B) $\frac { \sqrt { 6 } + \sqrt { 2 } } { 4 }$
C) $\frac { \sqrt { 2 } - \sqrt { 6 } } { 4 }$
D) $\frac { \sqrt { 6 } - \sqrt { 2 } } { 4 }$

Question

Quizplus · Accepted Answer

The expression $\sin \left( \frac { 17 \pi } { 12 } \right)$ can be rewritten using the addition formula for sine as $\sin \left( \frac { 3 \pi } { 4 } + \frac { \pi } { 3 } \right)$. This simplifies to $\sin \left( \frac { 3 \pi } { 4 } \right) \cos \left( \frac { \pi } { 3 } \right) + \cos \left( \frac { 3 \pi } { 4 } \right) \sin \left( \frac { \pi } { 3 } \right)$, which equals $\frac{\sqrt{2}}{2} \cdot \frac{1}{2} + \left(-\frac{\sqrt{2}}{2}\right) \cdot \frac{\sqrt{3}}{2}$, resulting in $- \frac { \sqrt { 6 } + \sqrt { 2 } } { 4 }$.

Use the Appropriate Addition Formula to Find the Exact Value sin⁡(17π12)\sin \left( \frac { 17 \pi } { 12 } \right)sin(1217π​)

Use the Appropriate Addition Formula to Find the Exact Value $\sin \left( \frac { 17 \pi } { 12 } \right)$