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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