Construction of the angle 
produces a 30-60-90 triangle, which has angles 
and 
. From the above diagram, write 
for the vertical leg, then the horizontal leg is given by
 | (1) |
by the Pythagorean theorem. Now use the double-angle formula
 | (2) |
to obtain
 | (3) |
which can be solved for 
to yield
 | (4) |
Filling in the rest of the trigonometric functions then gives
 |  |  | (5) |
 |  |  | (6) |
 |  |  | (7) |
 |  |  | (8) |
 |  |  | (9) |
 |  |  | (10) |
