Rotation without Imaginary Numbers, Transcendental Functions, or Infinite Sums

Quaterns are introduced as a new measure of rotation. Rotation in quaterns has an advantage that only simple algebra is required to convert back and forth between rectangular polar coordinates use the angle measure. All analogue trigonometric functions also become algebraic when angles expressed quaterns. This paper will show how quatern can be easily used approximate first quadrant without recourse technology, infinite sums, imaginarynumbers, or transcendental functions. Using these approximations applied all four quadrants any degree accuracy. shown by approximating \(\pi\) accuracy desired reference traditional at all.