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?
(In reply to Thoughts and Possible Solution
"Calculator uses degrees as default. By switching the calculator to read radians, the values converge to those found by Excel. However, when switching back to degrees, it still returns the values I mentioned before. This is quite puzzling."
It's to be expected that doing the iteration while the calculator is in degree mode would result in a different answer from when it's in radian mode. I'd expect that radian mode would be the one intended, as that is mathematically more naturally defined.
Take for example C: it's the cosine of a sine, and therefore the cosine of a number whose absolute value is at most 1. There's quite a difference between 1 degree and 1 radian.
I don't know why your calculator would not converge to better than 6 positions when working in radians. Unless you're not going far enough--40 iterations (80 button presses) should get you 12 decimal places.
Posted by Charlie
on 2005-11-08 15:57:17