Prove that arctan
(4*pi/3), in radians, is irrational.
arctan(a)=b implies that a is a ratio of the form y/x and b is an angle. Specifically it the the angle formed by the positive x-axis and the ray from (0,0) through (x,y).
It is rather strange that the given ratio is an expression containing pi, usually it is the angle that would be a rational multiple of pi.
As such I would surprised to see that the arctangent of any rational multiple of pi was rational.
The problem does not ask for tan(4pi/3) which is clearly an irrational number: the negative square root of 2.
Posted by Jer
on 2011-05-02 15:11:04