Any triangle, Trigonometric function - second episode! (Posted on 2007-11-18)

	Submitted by Chesca Ciprian
Rating: 3.0000 (1 votes)
Solution:	(Hide)
Like in the first episode - see "Acute triangle, trigonometric function!" if we take on the graph of the function f(x) = cos(x) a point A(x,cos(x)) there will take shape between origin and and the point B(pi/2,1) 2 triangles and 1 trapezium. The area of the trapezium and one triangle is bigger than the area of the last triangle. After calculus we find that cos(x)>=1-2x/pi. Using this relation for the angle's of an acute triangle we find that cos(A)+cos(B)+cos(C) > 1

	Subject	Author	Date
	re(2): Solution	Charlie	2007-11-21 09:10:11
	No Subject	Praneeth	2007-11-21 02:50:04
	Idea, observation and a nice solution!	Chesca Ciprian	2007-11-20 14:51:01
	re: Solution	Brian Smith	2007-11-20 12:03:23
	re: Solution	Charlie	2007-11-20 09:36:16
	Solution	Praneeth	2007-11-20 06:26:28
	re(3): non-Euclidean case?	brianjn	2007-11-19 07:58:10
	re(2): non-Euclidean case?	Dej Mar	2007-11-19 07:33:47
	re: non-Euclidean case?	brianjn	2007-11-19 06:59:34
	non-Euclidean case?	Dej Mar	2007-11-19 04:50:37
	computer exploration of all angles	Charlie	2007-11-18 23:16:28
	non-obtuse case	Dennis	2007-11-18 15:21:40