how can i derive the trigonometric functions from a unit circle?

1- Let x be a real number and P(x) a point on a unit circle such that the angle in standard position whose terminal side is segment OP is equal to x radians.(O is the origin of the system of axis used).

2- We define sin(x) as the y-coordinate of point P(x) on the unit circle.

3- We define cos(x) as the x-coordinate of a point P(x) on the unit circle.

4- We define tan(x) as the ratio of the y-coordinate and x-coordinate of point P(x) on a unit circle.