Simplify the given expression algebraically.
$$\cos ( \pi + x )$$
A) $\sin x$
B) $- \sin x$
C) $\cos x$
D) $- \cos x$
E) 1

Question

Quizplus · Accepted Answer

The cosine function has a period of $2\pi$ and is an even function, meaning $\cos(-x) = \cos(x)$. Using the sum formula for cosine, $\cos(\pi + x) = \cos(\pi)\cos(x) - \sin(\pi)\sin(x)$. Since $\cos(\pi) = -1$ and $\sin(\pi) = 0$, this simplifies to $-\cos(x)$.

Simplify the Given Expression Algebraically cos⁡(π+x)\cos ( \pi + x )cos(π+x)

Simplify the Given Expression Algebraically $\cos ( \pi + x )$