Does anyone know the limit of 1/sin(x) as x approaches pi?

Question

The problem shows as follows:

lim_x→π 1/sin(x)

If it does not exist, does anyone know why?

Answer 1

This limit does not exist because its value is different coming from the right and left side. Notice that

lim_x→π-1/sin(x) = ∞, and

lim_x→π+1/sin(x) = -∞

You can use a graph or a table to verify this result.