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!

Proving: limit (as theta approaches zero) of sin(theta)/(theta) = 1

  1. Mar 8, 2010 #1
    1. The problem statement, all variables and given/known data
    show that the limit as h approaches zero of ((cosh-1)/h) = 0.

    2. Relevant equations

    *The bold numbers preceding each line are simply line numbers, they are not apart of the equations.*

    1 lim (as h approaches 0) of ((cosh - 1)/h)

    2 = lim (as h approaches 0) of -((2sin2(h/2))/h)

    3 = -lim as theta approaches zero of ((sin[tex]\Theta[/tex]/[tex]\Theta[/tex])*sin[tex]\Theta[/tex]

    4 = -(1)(0)

    5 = 0

    I'm confused as to how the author of the text was able to get from line 1 to line 2. If someone could workout the steps between these two lines I would be appreciative. I'm drawing a blank here!

  2. jcsd
  3. Mar 8, 2010 #2


    Staff: Mentor

    The author used this identity: cos(2x) = cos2(x) - sin2(x) = 1 - 2sin2(h), and then replaced 2x by h.
  4. Mar 8, 2010 #3
    Ah, I see. Thank you.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook