# How do you simplify sin(x+pi)?

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#### Explanation

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Jim G. Share
Jul 31, 2016

$- \sin x$

#### Explanation:

Using $\textcolor{b l u e}{\text{addition formula for sin}}$

$\textcolor{red}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{\sin \left(A + B\right) = \sin A \cos B + \cos A \sin B} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

$\Rightarrow \sin \left(x + \pi\right) = \sin x \cos \pi + \cos x \sin \pi$

now $\cos \pi = - 1 \text{ and } \sin \pi = 0$

$\Rightarrow \sin x \cos \pi + \cos x \sin \pi = - \sin x + 0$

$\Rightarrow \sin \left(x + \pi\right) = - \sin x$

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