What is the limit as x approaches 2pi of (x-2pi)/(sin(x)) ?

The limit as x approaches 2pi of (x-2pi)/(sin(x)) is 1

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limit as x approaches 2pi of (x-2pi)/(sin(x))

x \to 2 π lim (\frac{x - 2 π}{sin ( x )})

1

Solution steps

x \to 2 π lim (\frac{x - 2 π}{sin ( x )})

Apply L'Hopital's Rule

= x \to 2 π lim (\frac{1}{cos ( x )})

Plug in the value

x = 2 π

= \frac{1}{cos ( 2 π )}

Simplify

\frac{1}{cos ( 2 π )} : 1

= 1

What is the limit as x approaches 2pi of (x-2pi)/(sin(x)) ?
The limit as x approaches 2pi of (x-2pi)/(sin(x)) is 1