Plane trigonometry, by S.L. Loney.

70

TRIGONOMETRY.

Exs. The supplement of 30~= 180 - 30~= 150~.
The supplement of 120~= 180~ - 120~= 60~.
The supplement of 275~= 180~ - 275~= - 95~.
The supplement of - 126~= 180~ - (- 126~) = 306~.
72. To find the values of the trigonometrical ratios of
the angle (180~ - 0) in terzs of those of the angle, for alt
values of 0.

A

Let the revolving line start from OA and describe any
angle AOP (= 0).
To obtain the angle 180~- 0, let the revolving line
start from OA and, after revolving through two right
angles (i.e. into the position OA'), then revolve back
through an angle 0 into the position OP', so that the angle
A'OP' is equal in magnitude but opposite in sign to the
angle AOP.
The angle AOP' is then 180~- 0.