Given an arc AM = x , with origin A and extremity M, that rotates on the trig unit circle with origin O.
The value of cos x is given by the projection of M on the horizontal OAx. Om = cos x.
The value of sin x is given by the projection of M on the vertical OBy axis. On = sin x. B is the top point of the trig circle.
Prolong the radius OM until it meets the vertical axis AT at t. the segment At = tan x.
Prolong the radius OM until it meets the horizontal BZ at z. The segment Bz = cot x.
In summary, the trig unit circle defines 4 trig functions of the arc AM = x. When the arc extremity M rotates, each function: f(x) = cos x; f(x) = sin x; f(x) = tan x; and f(x) = cot x varies along its own axis.
For example, the function f(x) = sin x varies from 1 to -1 then back to 1 on the horizontal OAx axis.
For example, the function f(x) = tan x varies from 0 to +infty on the vertical AT axis, when x varies from 0 to pi/2. And f(x) = tan x varies from -infty to 0 when x moves from pi/2 to pi.