trignometric limits?

Question

What is the limit of

lim(x approaches negative infinity) tan(inverse) x ?

the limit exists, i just dont know what it is

Answer 1

It's -pi/2.

As y->-pi/2 from the right, tan(y) -> -infinity. Since the range of inverse tangent is -pi/2 < tan(inverse) x < pi/2, you can see that the limit is -pi/2 by flipping the graph of x=tan(y), for -pi/2 < x < pi/2, to obtain the graph of y=tan(inverse) x.