Use a sum or difference identity to find the exact value.
-$$\sin \frac { 7 \pi } { 12 }$$
A) $\frac { 1 } { 2 }$
B) $\frac { \sqrt { 3 } + 1 } { 2 }$
C) $\frac { \sqrt { 6 } - \sqrt { 2 } } { 4 }$
D) $\frac { \sqrt { 6 } + \sqrt { 2 } } { 4 }$

Question

Quizplus · Accepted Answer

The exact value of $\sin \frac { 7 \pi } { 12 }$ can be found by using the sum identity $\sin(a + b) = \sin a \cos b + \cos a \sin b$, where $a = \frac{\pi}{4}$ and $b = \frac{\pi}{3}$, thus $\sin \frac { 7 \pi } { 12 } = \sin(\frac{\pi}{4} + \frac{\pi}{3}) = \sin \frac{\pi}{4} \cos \frac{\pi}{3} + \cos \frac{\pi}{4} \sin \frac{\pi}{3} = \frac{\sqrt{2}}{2} \cdot \frac{1}{2} + \frac{\sqrt{2}}{2} \cdot \frac{\sqrt{3}}{2} = \frac{\sqrt{2}}{4} + \frac{\sqrt{6}}{4} = \frac{\sqrt{6} + \sqrt{2}}{4}$.

Use a Sum or Difference Identity to Find the Exact sin⁡7π12\sin \frac { 7 \pi } { 12 }sin127π​

Use a Sum or Difference Identity to Find the Exact $\sin \frac { 7 \pi } { 12 }$