Use a sum or difference identity to find the exact value.
-$\sin ( x + 2 \pi )$
A) $- \cos x$
B) $\frac { \sqrt { 2 } } { 2 } \cos x + \frac { \sqrt { 2 } } { 2 } \sin x$
C) $\sin x$
D) $\frac { \sqrt { 2 } } { 2 } \cos x - \frac { \sqrt { 2 } } { 2 } \sin x$

Question

Quizplus · Accepted Answer

The sum identity for sine is $\sin(a + b) = \sin a \cos b + \cos a \sin b$. Since $\sin(2\pi) = 0$ and $\cos(2\pi) = 1$, $\sin(x + 2\pi) = \sin x \cdot 1 + \cos x \cdot 0 = \sin x$.

Use a Sum or Difference Identity to Find the Exact sin⁡(x+2π)\sin ( x + 2 \pi )sin(x+2π)

Use a Sum or Difference Identity to Find the Exact $\sin ( x + 2 \pi )$