on the integral
But how do I find out these two calculations below without using a calculator?
For and construct an equilateral triangle (all three side of equal length so all three angles congruent so each angle ) with sides of length 2 and draw a line from one vertex perpendicular to the opposites side. By symmetry (that line divides the equilateral triangle into two congruent right triangles) we have a right triangle with one angle , another angle , hypotenuse of length 2 and side opposite the [tex]\pi/6[itex] angle of length 1. By the Pythagorean theorem the other leg (opposite the angle and the perpendicular constructed) has length .
From that, we have , and , .