y The angle α is 30◦ in the example (π/6 in radians). The sine of α, which is the height of the red line, is
1
sin α = 1/2.
1 2
tan α =
sin α α −1
cos α
− 21 − 12
sin α cos α x
1
By the Theorem of Pythagoras we have cos2 α + sin2 α = 1. Thus the length of the blue line, which is the cosine of α, must be p √ cos α = 1 − 1/4 = 12 3. This shows that tan α, which is the height of the orange line, is
−1 tan α =
√ sin α = 1/ 3. cos α