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Trigonometry Nest 2 (Posted on 2005-11-07)

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?

Submitted by Larry

Rating: 3.0000 (2 votes)

Solution: (Hide)

a)
C(x) is approx. 0.76816916
S(x) is approx. 0.69481969
b) I haven't found a solution to this. But I have an idea:
note that C(x) = cos(sin(C(x))
Arccos(C(x)) = Sin(C(x))
Therefore if you plot out Arccos(t) and Sin(t), the value of C(x) should be the y value of where those two curves cross each other.

Similarly S(x) = sin(cos(S(x))
So the value of S(x) should be the y value of the point where these two functions meet: Arcsin(t) and Cos(t)

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
approx. values of...	Norma	2007-01-11 18:51:52
A few minutes and a calculator (solution)	Leon	2005-11-17 18:51:31
re: Thoughts and Possible Solution	Charlie	2005-11-08 15:57:17
Thoughts and Possible Solution	Alexis	2005-11-07 23:48:09
some thoughts--spoiler present	Charlie	2005-11-07 10:49:43
To greater precision	Charlie	2005-11-07 10:37:33
Excel spoiler	Steve Herman	2005-11-07 10:22:32

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