Plane trigonometry, by S.L. Loney.

120

TRIGONOMETRY.

It is negative otherwise.
The results of this article are shewn graphically in the
following figure.

B'

OA is the initial line and OP, OQ, OR and OS bisect
the angles in the first, second, third and fourth quadrants
respectively.
Numerical Example. Within what limits must - lie if
2 sin= - /1+sin A - "/ 1- sin A.
In this case the formulae of Art. 113 must clearly be
A A
sin + cos - = - J sin A..................... (1),
2 2
and sin 2 - 1co = - - sin A....................(2).
For the addition of these two formulae gives the given formula.
From (1) it follows that the revolving line which bounds the angle 2
must be between OQ and OR or else between OR and OS.