One of the motivations for developing trigonometry with a unit circle is that you can actually see sin and cos on the circle.

One of the motivations for developing trigonometry with a unit circle is that you can actually “see” sin θ and cos θ on the circle. Note in the following figure that AP = sin θ and OA = cos θ. It turns out that you can also “see” the other four trigonometric functions. Prove each of the following.

a) BD = tan θ 

b) OD = sec θ

c) OE = csc θ 

d) CE = cot θ

C 1- O 0 P E D A B X