Location, Trigonometry, and Measurement of the Sphere - Spatial Mathematics: Theory and Practice through Mapping - page 48

co-axis co-axis

(a) (b)

(0,1)

(0,1)

P P

co- θ

θ θ

(0,0) axis

(1,0) (0,0) (1,0) axis

co-axis co-axis

(c) (d)

(0,1) (0,1)

P P

co- θ

θ

(1,0) axis (0,0) (1,0) axis

(0,0)

Figure 2.3 (a) Unit circle, axis, and complementary (orthogonal) axis designated
as co-axis. A secant line intersects the circle at P and forms an angle of θ with the
axis and an angle of co- θ with the co-axis. (b) Derivations of sine (green), tangent
(red), and secant (blue) functions of angle θ . (c) Derivations of co-sine (green),
co-tangent (red), and co-secant (blue) functions of co-angle θ . (d) Shows right tri-
angle interpretation of cosine as adjacent side over hypotenuse. Source: Modified
from Arlinghaus, S. L. and W. C. Arlinghaus, 2005. Spatial Synthesis: Centrality
and Hierarchy. Volume I, Book 1. http://www.imagenet.org , Introduction. QR code
links to animation from that book, http://www-personal.umich.edu/~copyrght/
image/books/Spatial%20Synthesis/trig/anisandytrig.gif