Use the fundamental identities to simplify the expression.
-$\sin \frac { 11 \pi } { 12 }$
A) $\frac { \sqrt { 6 } - \sqrt { 2 } } { 4 }$
B) $\frac { \sqrt { 6 } + \sqrt { 2 } } { 4 }$
C) $\frac { \sqrt { 3 } - 2 } { 4 }$
D) $\frac { \sqrt { 3 } + 2 } { 4 }$

Question

Quizplus · Accepted Answer

$\sin \frac { 11 \pi } { 12 }$ can be simplified using the sum or difference formula for sine: $\sin(a \pm b) = \sin a \cos b \pm \cos a \sin b$. Here, $\frac { 11 \pi } { 12 } = \frac { 9 \pi } { 12 } + \frac { 2 \pi } { 12 } = \frac { 3 \pi } { 4 } + \frac { \pi } { 6 }$. Thus, $\sin \frac { 11 \pi } { 12 } = \sin \frac { 3 \pi } { 4 } \cos \frac { \pi } { 6 } + \cos \frac { 3 \pi } { 4 } \sin \frac { \pi } { 6 }$, which simplifies to $\frac { \sqrt { 6 } - \sqrt { 2 } } { 4 }$.

Use the Fundamental Identities to Simplify the Expression sin⁡11π12\sin \frac { 11 \pi } { 12 }sin1211π​

Use the Fundamental Identities to Simplify the Expression $\sin \frac { 11 \pi } { 12 }$