# Limit of a trig function

1. Oct 20, 2009

### physicsman2

1. The problem statement, all variables and given/known data
lim as x approaches pi

(pi-x)/sin(x)

2. Relevant equations

above equation

3. 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

2. Oct 20, 2009

### lanedance

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

x = t+ pi

t/sin(t+pi)

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

3. Oct 20, 2009

### physicsman2

thank you

4. Oct 20, 2009

### Staff: Mentor

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).

5. Oct 20, 2009

### lanedance

yeah thats cleaner

6. Oct 20, 2009

### physicsman2

yeah, i saw that

thank you to the both of you