Plane trigonometry, by S.L. Loney.

CHANGES IN THE TRIGONOMETRICAL RATIOS.

53

When it coincides with OA the
length OM, is equal to a and, B Pi
when it coincides with OB, the \ /
point M, coincides with 0 and OM
vanishes. Also, as the revolving A' M IM4 A
line turns from OA to OB, the distance OMA decreases from a. to
P3 _ P4
zero. B'
Whilst the revolving line is in
the second quadrant and is revolving from OB to OA', the
distance OM, is negative and increases numerically from
0 to a [i.e. it decreases algebraically from 0 to -a].
In the third quadrant the distance OM:s increases
algebraically from - a to 0, and in the fourth quadrant
the distance OM4 increases from 0 to a.
In the first quadrant the length MlP, increases from
0 to a; in the second quadrant M2P2 decreases from a to
O; in the third quadrant M3P3 decreases algebraically
from 0 to - a; whilst in the fourth quadrant M4P4
increases algebraically from - a to 0.
54. Sine. In the first quadrant as the angle increases from 0 to 90", the sine, i:e. M1_, increases from -
a a
to -, i.e. from 0 to 1.
a
In the second quadrant as the angle increases from
90~ to 180~, the sine decreases from - to -, i.e. from 1 to 0.
a a
In the third quadrant as the angle increases from 180~
to 270~, the sine decreases from - to-, i.e. from 0 to - 1.
a a