Find the exact value of the given expression using a sum or difference formula. $\sin 345 ^ { \circ }$
A) $\frac { \sqrt { 3 } + 1 } { 2 \sqrt { 2 } }$
B) $\frac { \sqrt { 3 } - 1 } { 2 \sqrt { 2 } }$
C) $\frac { - \sqrt { 3 } + 1 } { 2 \sqrt { 2 } }$
D) $\frac { - \sqrt { 3 } - 1 } { 2 \sqrt { 2 } }$

Question

Quizplus · Accepted Answer

$\sin 345^\circ = \sin(360^\circ - 15^\circ) = -\sin 15^\circ$. Using the half-angle formula, $\sin 15^\circ = \sin(30^\circ/2) = \frac{\sqrt{2 - \sqrt{3}}}{2}$. Therefore, $\sin 345^\circ = -\frac{\sqrt{2 - \sqrt{3}}}{2} = \frac{-\sqrt{3} + 1}{2\sqrt{2}}$.

Find the Exact Value of the Given Expression Using a Sum