19 Jul
2006
19 Jul
'06
11:09 a.m.
On Wednesday 19 July 2006 03:43, Alec Mihailovs wrote:
In addition to Richardson's method that I briefly described at the beginning of the thread, another not very often used approach is to use better than sin(x)<x<tan(x) inequalities.
For example,
sin(x)*(14+cos(x))/(9+6*cos(x)) < x < 8*sin(x)/9/(1+cos(x))+25*sin(x)/(36+9*cos(x))
Are these less painful to find and prove than they look? :-) (I suppose you'd prove them by clearing denominators, expressing everything in terms of sin(kx) and cos(kx), and comparing terms in the Taylor series, or something like that. How do you find them?) -- g