The power of the percent (decimal point) based unit circle is logical not mystical. Y is the Sine, X is the Cosine and the percent of rotation times 2Pi is the radian value of the angle theta.
An angle is a percentage of the circumference of a circle (inscribed arc).
The ancient Babylonians with their sexagesimal (base 60 system) used 60*6 or 360° to represent a circle. It is evenly divisible by 2,3,4,5,6,8,9,10, and 12 (a lot of ways to cut a pie). It is similar to the clock system so 1°, like 1, hour can be divided by 60' minutes and a minute can be divided by 60" seconds. This use of sexagesimal angular degrees is still used in astronomy and geography. It is called the Degree Minute Second (DMS) system. The degree decimal system (dd) is frequently used in trigonometry. The radian system is a circumference/radius system.
1 radian=circumference/radius. Circles have radiuses. Right triangles have hypotenuses. The unit circle circumference based system is the simplest way to work with radians because the hypotenuse is the radius, and it equals 1. The circumference of the unit circle is 2*PI*1. An angle in radians can be defined as its arc length (the intercepted arc of the inscribed angle) on a unit circle's circumference. That value is the percent of counter clockwise rotation times 2Pi.
The site also includes downloadable factorial and n choose k functions.
Please check out the regular and irregular polygon functions, the fractal triangles and Koch snowflakes.