Use Identities to find the exact value.
-$\sin \left( x + 45 ^ { \circ } \right)$
A) $\sin x$
B) $\frac { \sqrt { 2 } } { 2 } \cos x + \frac { \sqrt { 2 } } { 2 } \sin x$
C) $- \cos x$
D) $\frac { \sqrt { 2 } } { 2 } \cos x - \frac { \sqrt { 2 } } { 2 } \sin x$

Question

Quizplus · Accepted Answer

The correct answer is obtained by using the sine addition formula: $\sin(a + b) = \sin a \cos b + \cos a \sin b$. Substituting $a = x$ and $b = 45^\circ$, and knowing that $\sin 45^\circ = \cos 45^\circ = \frac{\sqrt{2}}{2}$, we get $\frac{\sqrt{2}}{2}\cos x + \frac{\sqrt{2}}{2}\sin x$.

Use Identities to Find the Exact Value sin⁡(x+45∘)\sin \left( x + 45 ^ { \circ } \right)sin(x+45∘)

Use Identities to Find the Exact Value $\sin \left( x + 45 ^ { \circ } \right)$