All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Just Math
Trigonometry Nest 2 (Posted on 2005-11-07) Difficulty: 1 of 5
In Trigonometry Nest, the functions sin(cos(x)) and cos(sin(x)) were introduced, and it was proven that one of these functions is always greater than the other.

Taking this concept to infinity, which of these functions is greater: C(x)=cos(sin(cos(......(sin(x))))...))), or S(x)=sin(cos(sin(......(cos(x))))...)))?

How does the ratio C(x)/S(x) depend on x?

See The Solution Submitted by Larry    
Rating: 3.0000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Some Thoughts Excel spoiler | Comment 1 of 7
As long as nobody was commenting, I thought I'd try it in excel, just to see whether it really converged.

In fact, it seems to converge pretty quickly.

I have C(x) approximates .768169 for all x
           S(x) approximates .694820 for all x

C(x) is greater

  Posted by Steve Herman on 2005-11-07 10:22:32
Please log in:
Remember me:
Sign up! | Forgot password

Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (3)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Copyright © 2002 - 2019 by Animus Pactum Consulting. All rights reserved. Privacy Information