Plane trigonometry with practical applications, by Leonard E. Dickson.

CHAPTER XI

GRAPHS OF THE TRIGONOMETRIC FUNCTIONS AND THEIR
INVERSES, RADIANS
106. Line representations of the trigonometric functions.
Consider any angle A in its trigonometric position and recall the
definitions (Art. 83) that sin A = y/r, cos A = x/r, etc., where
x and y are the coordinates of any point P of the terminal side of
angle A, while r is the distance from P to the origin 0. Since r
is the denominator of the fractions defining sin A and cos A, take
r = 1 for convenience, i.e., take OP as the unit of length of our
drawings. Then sin A is represented to scale by the ordinate y
(PF in Figs. 81, 82; -PF in Figs. 83, 84) and cos A is repref cot T cot Y
T
A cos X cos
0 F~X F o
T
FIG. 81 FIG. 82
sented by the abscissa x (OF in Figs. 81, 84; -OF in Figs. 82, 83).
Hence the sine of an angle in its trigonometric position is equal, in
magnitude and sign, to the ordinate of the point P in which the
terminal side of the angle intersects the unit circle. The cosine is
equal to the abscissa of P.
Next, consider tan A = y/x, where x 3 0. First, let A be in
the first or fourth quadrant, so that the abscissa x is positive.

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