What is the limit as x approaches 0 of x/(sin(x+pi)) ?

The limit as x approaches 0 of x/(sin(x+pi)) is -1

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limit as x approaches 0 of x/(sin(x+pi))

x \to 0 lim (\frac{x}{sin ( x + π )})

- 1

Solution steps

x \to 0 lim (\frac{x}{sin ( x + π )})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{1}{- cos ( x )})

= x \to 0 lim (\frac{1}{- cos ( x )})

Plug in the value

x = 0

= \frac{1}{- cos ( 0 )}

Simplify

\frac{1}{- cos ( 0 )} : - 1

= - 1

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What is the limit as x approaches 0 of x/(sin(x+pi)) ?
The limit as x approaches 0 of x/(sin(x+pi)) is -1