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: arctan equation?

  1. Nov 7, 2011 #1
    Can someone please let me know how to find x in

    π/4=arctan(x+arctan(x+...)) ?
     
  2. jcsd
  3. Nov 7, 2011 #2

    micromass

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    Let me do a similar one:

    Let [itex]x=\sqrt{2+\sqrt{2+\sqrt{2+...}}}[/itex]. Then [itex]x^2-2=x[/itex].
    Solving the quadratic equation gives us the answer.

    Can you do your problem now along similar lines??
     
  4. Nov 7, 2011 #3
    micromass: isn't it the use of inverse operator (tan in this case)?
    like z=arctan(x+arctan(x+...)) and make the use of tanz?

    and then use tan addition rule??? I am really confused...

    Can you explain further please?
     
  5. Nov 7, 2011 #4

    lurflurf

    User Avatar
    Homework Helper

    π/4=arctan(x+arctan(x+...))
    take tan of both sides
    tan(π/4)=tan(arctan(x+arctan(x+...)) )
     
  6. Nov 7, 2011 #5
    lurflurf: and then what?

    tan(π/4) = x + arctan(x+arctan(x+...)) ???
     
  7. Nov 7, 2011 #6
    what is tan(tanx)??? Is above equation some kind of sum of geometric progress???
     
  8. Nov 7, 2011 #7
    is it so easy that no one is going even to comment?
     
  9. Nov 7, 2011 #8

    lurflurf

    User Avatar
    Homework Helper

    tan(π/4)=tan(arctan(x+arctan(x+...)) )
    1=x+arctan(x+arctan(x+...))
     
  10. Nov 7, 2011 #9
    lurflurf: thank you, this is obvious and not the solution

    then

    tan(1-x) = x + arctan(x+arctan(x+...))

    and where it is leading???
     
  11. Nov 8, 2011 #10

    lurflurf

    User Avatar
    Homework Helper

    arctan(x+arctan(x+...)) ?
     
  12. Nov 8, 2011 #11
    if I knew what "arctan(x+arctan(x+...))" equals to, I wouldn't be posting this thread...
     
  13. Nov 8, 2011 #12
    What? You said what this equals in your first post. It's x that is the unknown.
     
  14. Nov 8, 2011 #13
    spamiam: right, sorry, I'm really dumb

    x = 1 - π/4

    Thank you all for bearing with me...
     
  15. Nov 8, 2011 #14
    This is dumbest question I have ever asked. Hope this is never going to happen again...
     
  16. Nov 8, 2011 #15
    You're not dumb--this question is difficult until you see the trick to use.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Trigonometry: arctan equation?
  1. Arctan identity? (Replies: 2)

  2. Basic trigonometry (Replies: 5)

Loading...