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!

Trigonometry - Cosec summation

  1. Oct 19, 2013 #1
    1. The problem statement, all variables and given/known data
    has the value equal to ##\cot\frac{\pi}{A}## then find A.

    2. Relevant equations

    3. The attempt at a solution
    Writing cosec in terms of sin and taking the LCM to make a common denominator doesn't seem to be of any help.

    I can find the value of each term but that would be tedious and of no use.

    I honestly cannot figure out how should I proceed here.

    Any help is appreciated. Thanks!
    Last edited: Oct 19, 2013
  2. jcsd
  3. Oct 19, 2013 #2


    User Avatar
    Science Advisor
    Homework Helper

    Try showing cot(x)-cot(2x)=csc(2x).
  4. Oct 19, 2013 #3

    Simon Bridge

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    ##\csc(\frac{\pi}{2})## appears twice.
    All the angles are successive doublings of ##\pi/32##
  5. Oct 19, 2013 #4
    Wow! Thanks a lot Dick! :smile:

    How did you come up with that?

    Very sorry for the typo, its ##\pi/8## instead of the second ##\pi/2##.
  6. Oct 19, 2013 #5


    User Avatar
    Science Advisor
    Homework Helper

    I guessed the series must telescope somehow. So somehow cot(2x) must be related to cot(x) with the difference related to a csc. Seems obvious in retrospect, yes?
    Last edited: Oct 19, 2013
  7. Oct 19, 2013 #6
    Yes. I liked the way you came up with cot(x)-cot(2x) and solved the problem in few seconds where I was stuck for a week.

    Thank you again! :)
  8. Oct 19, 2013 #7


    User Avatar
    Science Advisor
    Homework Helper

    You're welcome, but it took me more than a "few seconds". Still keeping that strategy in mind might help in the future. If you've got the sum of a bunch of csc's equaling a cot, then if you can express each csc as a difference of two cot's you might be able to sum the series easily. Substitute any other functions you want for 'csc' and 'cot'.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted

Similar Discussions: Trigonometry - Cosec summation
  1. Trigonometry expansion (Replies: 1)

  2. Trigonometry question (Replies: 6)

  3. A Trigonometry Problem (Replies: 15)

  4. Trigonometry Problem (Replies: 3)