# How do you find values of trigonometric functions using the unit circle?

Given an arc $A M = x$ , 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 $O A x$. $O m = \cos x$.
The value of $\sin x$ is given by the projection of $M$ on the vertical $O B y$ axis. $O n = \sin x$. $B$ is the top point of the trig circle.
Prolong the radius $O M$ until it meets the vertical axis $A T$ at $t$. the segment $A t = \tan x$.
Prolong the radius $O M$ until it meets the horizontal $B Z$ at $z$. The segment $B z = \cot x$.
In summary, the trig unit circle defines 4 trig functions of the arc $A M = x$. When the arc extremity $M$ rotates, each function: $f \left(x\right) = \cos x$; $f \left(x\right) = \sin x$; $f \left(x\right) = \tan x$; and $f \left(x\right) = \cot x$ varies along its own axis.
For example, the function $f \left(x\right) = \sin x$ varies from $1$ to $- 1$ then back to $1$ on the horizontal $O A x$ axis.
For example, the function $f \left(x\right) = \tan x$ varies from $0$ to $+ \infty$ on the vertical $A T$ axis, when $x$ varies from $0$ to $\frac{\pi}{2}$. And $f \left(x\right) = \tan x$ varies from $- \infty$ to $0$ when $x$ moves from $\frac{\pi}{2}$ to $\pi$.