Rotation without Imaginary Numbers, Transcendental Functions, or Infinite Sums

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