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 xaxis 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.
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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 20110502 15:11:04 