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      Hello,
pi-r-fun.com advocates a counter clockwise rev, the unit circle, and the polar coordinate system as the simplest approach to trigonometry, and pi-r-fun.com advocates the synergy of trigonometry and JavaScript.
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.
Some engineering fields use the floating point value "rev" to represent "rotation" or "turn". But these terms represent clockwise rotation. Most unit circles are counter clockwise with 90˚ and Pi/2 at the apex. pi-r-fun.com advocates a counter clockwise decimal point based rev as the simplest approach to trigonometry, and pi-r-fun.com advocates the synergy of trigonometry and JavaScript.
The caveat: JavaScript trig functions require counter clockwise radian values and Scalable Vector Graphics require clockwise degree values for the rotate transform!
Scalable Vector Graphics enables graphics to look smooth (no jaggies) on any size display. JavaScript with it's trig functions and loop structures is useful for generating SVG.
Pi-r-fun.com provides a downloadable unit circles marked by 1% (.01) increments and 5˚ increments, an explanation and comparison of the Cartesian coordinate and screen coordinate systems. pi-r-fun.com provides JavaScript code for the creation of Cartesian coordinate systems on HTML and SVG canvasses. The site includes a downloadable JavaScript functions (in .txt format,load into editor save as .html or .js) that will allow placement of regular and irregular polygons anywhere on HTML and SVG canvasses. The graphics at the top of this page were created using those polygon functions.
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.
Thanks,
marc@pi-r-fun.com



unit circle