Simplify the expression algebraically.
$8 \sin \left( \frac { \pi } { 2 } + x \right)$
A) $- 8 \cos x$
B) $\frac { 1 } { 8 } \cos x$
C) $8 \cos x$
D) $8 \sin x$
E) $- \frac { 1 } { 8 } \cos x$

Question

Simplify the expression algebraically. 
$8 \sin \left( \frac { \pi } { 2 } + x \right)$
A) $- 8 \cos x$
B) $\frac { 1 } { 8 } \cos x$
C) $8 \cos x$
D) $8 \sin x$
E) $- \frac { 1 } { 8 } \cos x$

Quizplus · Accepted Answer

Using the trigonometric identity $\sin(a + b) = \sin a \cos b + \cos a \sin b$, we can simplify $8 \sin \left( \frac { \pi } { 2 } + x \right)$ to $8(\sin \frac{\pi}{2} \cos x + \cos \frac{\pi}{2} \sin x)$. Since $\sin \frac{\pi}{2} = 1$ and $\cos \frac{\pi}{2} = 0$, the expression simplifies to $8 \cos x$.

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Simplify the Expression Algebraically $8 \sin \left( \frac { \pi } { 2 } + x \right)$