Use the Half-angle Formulas to find the exact value of the trigonometric function.
-$$\sin \frac { 5 \pi } { 12 }$$
A) $- \frac { 1 } { 2 } \sqrt { 2 + \sqrt { 3 } }$
B) $\frac { 1 } { 2 } \sqrt { 2 - \sqrt { 3 } }$
C) $\frac { 1 } { 2 } \sqrt { 2 + \sqrt { 3 } }$
D) $- \frac { 1 } { 2 } \sqrt { 2 - \sqrt { 3 } }$

Question

Quizplus · Accepted Answer

To find $\sin \frac { 5 \pi } { 12 }$, we can use the half-angle formula for sine, $\sin \frac{\theta}{2} = \pm \sqrt{\frac{1 - \cos \theta}{2}}$, with $\theta = \frac{5\pi}{6}$ because $\frac{5\pi}{12}$ is half of $\frac{5\pi}{6}$. We know that $\cos \frac{5\pi}{6} = -\sqrt{3}/2$. Substituting this into the formula gives $\sin \frac { 5 \pi } { 12 } = \sqrt{\frac{1 - (-\sqrt{3}/2)}{2}} = \frac { 1 } { 2 } \sqrt { 2 + \sqrt { 3 } }$.

Use the Half-Angle Formulas to Find the Exact Value of the Trigonometric