What is the Limit of a Trig Function When x Approaches Pi?

[physicsman2]

Homework Statement

lim as x approaches pi

(pi-x)/sin(x)

Homework Equations

above equation

The Attempt at a Solution

well, i substituted pi-x for t
then took the limit as x approaches pi
got zero, so the equation is now

lim as t approaches 0

t/sin(x)

i know the answer is one, but how can i get it after this step

edit: i can't use l'hopital's rule

 

[lanedance]

if you want to substitute for x, you should do both

x = t+ pi

so your limit becomes
t/sin(t+pi)

you could try expanding sin in a taylor series if you can't use L'Hop

 

[physicsman2]

thank you

 

[Mark44]

Can you use the fact that \lim_{x \rightarrow 0}\frac{sin x}{x}~=~1?

If you can, you might also make use of the identity that sin(pi - x) = sin(x).

 

[lanedance]

yeah that's cleaner

 

[physicsman2]

yeah, i saw that

thank you to the both of you