Plane trigonometry, by S.L. Loney.

256 TRIGONOMETRY.
The angle BOC is -th of the sum of all the angles
subtended at 0 by the sides,
i.e. zLBOC4 4 right angles 27r di
i.e. Z BOC= — ~ ---~- = - radians.
In n
Hence Z BOL = z BOC=.
n
If a be a side of the polygon, we have
a = BC = 2BL = 2R sin BOL = 2R sin 7r.
a a wt'.. R = - =. cosec-...........(1).
7r 2 n
2 sinn
Again,
a = 2BL = 20L tan BOL = 2r tan.
a a w7
r=-=-cot-. (2)... r - - = 2 cot............. (2)
w 2 n
2 tan -
225. Area of a Regular Polygon.
The area of the polygon is n times the area of the
triangle BOC.
Hence the area of the polygon
= n x OL. BC = n. OL. BL =. BL cotLOB.BL
a2 7r
=n.- cot......
4 n (1),
giving the area in terms of the side.
Also the area
=n. OL. BL = n. OL. OL Otan BOL = nr2 tan 7t...(2).
nb