1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Limit of a trig function

  1. Oct 20, 2009 #1
    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. jcsd
  3. Oct 20, 2009 #2

    lanedance

    User Avatar
    Homework Helper

    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
     
  4. Oct 20, 2009 #3
    thank you
     
  5. Oct 20, 2009 #4

    Mark44

    Staff: Mentor

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

    If you can, you might also make use of the identity that sin(pi - x) = sin(x).
     
  6. Oct 20, 2009 #5

    lanedance

    User Avatar
    Homework Helper

    yeah thats cleaner
     
  7. Oct 20, 2009 #6
    yeah, i saw that

    thank you to the both of you
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Limit of a trig function
  1. Limit of trig function (Replies: 23)

Loading...