Plane trigonometry, by S.L. Loney.

56

TRIGONOMETRY.

from OA to OB, the quantity MiP, increases from 0 to a
and OMI decreases from a to 0.
Hence in the first quadrant the cotangent decreases
from c to O.
In the second quadrant M2P2 is positive and OM.2
— a
negative, so that the cotangent decreases from 0 to
i.e. from 0 to - o.
In the third quadrant it is positive and decreases from
oc to 0 [for as the revolving line crosses OB' the cotangent
changes from - oo to oo ].
In the fourth quadrant it is negative and decreases
from 0 to - oo.
58. Secant. When the revolving line coincides with
OA the value of OM1 is a, so that the value of the secant
is then unity.
As the revolving line turns from OA to OB, OM,
decreases from a to 0, and when the revolving line
coincides with OB the value of the secant is. i.e. oo.
0'
Hence in the first quadrant the secant increases from
1 to o.
In the second quadrant OM2 is negative and decreases
from 0 to-a. Hence in this quadrant the secant increases from - co to - 1 [for as the revolving line crosses
OB the quantity OM1 changes sign and therefore the
secant changes from + oo to - co ].
In the third quadrant OM3 is always negative and
increases from -a to 0; therefore the secant decreases
from- 1 to - o. In the fourth quadrant OM1 is always
positive and increases from 0 to a. Hence in this quadrant the secant decreases from so to + 1.