The Cosmic Game ( PDFDrive.com )

Cosmic Game © Douglass A. White, 2012 v151207 237
or cosine without infinitesimalizing to limits, and we have a clear understanding of how it
relates to a tangent point on a curve and a constant velocity. This is so much simpler
than the otherwise necessary division of 0 by 0 using the “ghosts of departed quantities”
as Berkeley so aptly described them.
The sketch below shows rotation by additional 90 degree steps into the third and fourth
quadrant. The oscillating nature of sine and cosine are obvious.
Sketch of an angle sum proof in trigonometry
(See Wikipedia)
Draw a horizontal line (the x-axis); mark an origin O. Draw a line from O at an angle
above the horizontal line and a second line at an angle above that; the angle between
the second line and the x-axis is .
Place P on the line defined by at a unit distance from the origin.
Let PQ be a line perpendicular to line defined by angle , drawn from point Q on this
line to point P. OQP is a right angle.
Let QA be a perpendicular from point A on the x-axis to Q and PB be a perpendicular
from point B on the x-axis to P. OAQ and OBP are right angles.
Draw QR parallel to the x-axis.
Now angle (because , making