Plane trigonometry, by S.L. Loney.

50

TRIGONOMETRY.

out an angle of any magnitude whatever. From a
point P in the revolving line draw PM perpendicular
to AOA'.
[Four positions of the revolving line are given in the figure, one in
each of the four quadrants, and the suffixes 1, 2, 3 and 4 are attached to
P for the purpose of distinction.]
We then have the following definitions, which are the
same as those given in Art. 23 for the simple case of an
acute angle:
MP
OP is called the Sine of the angle A OP,
OM
0111t
~Op:~, Cosine
MP
1OM Tangent,
01M
-MP I ~, Cotangent
OP
OQP I ~ Secant
OP
AlOP I I Cosecant
The quantities 1 - cos AOP, and 1 - sin AOP are
respectively called the Versed Sine and the Coversed
Sine of A OP.
51. In exactly the same manner as in Art. 27 it may
be shewn that, for all values of the angle AOP (= 0), we
have