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

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

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

x \to π lim (sin (\frac{x}{2} - π))

- 1

Solution steps

x \to π lim (sin (\frac{x}{2} - π))

Plug in the value

x = π

= sin (\frac{π}{2} - π)

Simplify

sin (\frac{π}{2} - π) : - 1

= - 1

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