Trigonometry: arctan equation?

In summary, the conversation is about finding the value of x in π/4=arctan(x+arctan(x+...)) by using similar methods to the problem x=\sqrt{2+\sqrt{2+\sqrt{2+...}}}. It involves taking the tangent of both sides and using the tangent addition rule. The final solution is x = 1 - π/4.
  • #1
21
0
Can someone please let me know how to find x in

π/4=arctan(x+arctan(x+...)) ?
 
Mathematics news on Phys.org
  • #2
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??
 
  • #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?
 
  • #4
π/4=arctan(x+arctan(x+...))
take tan of both sides
tan(π/4)=tan(arctan(x+arctan(x+...)) )
 
  • #5
lurflurf: and then what?

tan(π/4) = x + arctan(x+arctan(x+...)) ?
 
  • #6
what is tan(tanx)? Is above equation some kind of sum of geometric progress?
 
  • #7
is it so easy that no one is going even to comment?
 
  • #8
tan(π/4)=tan(arctan(x+arctan(x+...)) )
1=x+arctan(x+arctan(x+...))
 
  • #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?
 
  • #10
arctan(x+arctan(x+...)) ?
 
  • #11
if I knew what "arctan(x+arctan(x+...))" equals to, I wouldn't be posting this thread...
 
  • #12
XYZ313 said:
if I knew what "arctan(x+arctan(x+...))" equals to, I wouldn't be posting this thread...

What? You said what this equals in your first post. It's x that is the unknown.
 
  • #13
spamiam: right, sorry, I'm really dumb

x = 1 - π/4

Thank you all for bearing with me...
 
  • #14
This is dumbest question I have ever asked. Hope this is never going to happen again...
 
  • #15
You're not dumb--this question is difficult until you see the trick to use.
 

Suggested for: Trigonometry: arctan equation?

Replies
2
Views
646
Replies
3
Views
737
Replies
5
Views
982
Replies
3
Views
753
Replies
22
Views
2K
Replies
4
Views
728
Replies
5
Views
709
Replies
8
Views
1K
Replies
1
Views
1K
Back
Top