Whats the quickest way to determine trig functions of radian measures?
Is this a trick question? You’ve specified you can’t use a pencil or paper, but you say nothing about using a calculator. The quickest way, therefore, is likely to be by using a calculator. However, if you wish to do it in your head, 2Pi/3 radians is equivalent to 60 degrees, and sine of 60 degrees is simple. It’s sqrt(3) / 2, as described below: A triangle with an angle of 60 degrees at each corner will have sides of equal length. For convenience, call that length 2. Therefore, if you bisect one of the angles, the line will cross the side of the triangle at 90 degrees, hence bisecting that side into two equal lengths. Therefore, the hypotenuse will be 2, the adjacent side will be 1, and therefore, by Pythagoras’s Theorem, the opposite side will be the square root of 3.
