Plane trigonometry, by S.L. Loney.

6

TRIGONOMETRY.

The unit used is obtained thus;
Take any circle APBB', whose centre
any point A measure off an arc
AP whose length is equal to the
radius of the circle. Join OA and /
OP.

is 0, and from

B

The angle A OP is the angle
which is taken as the unit of circular measurement, i.e. it is the
angle in terms of which in this
system we measure all others.
This angle is called A Radian
by 1.

A

and is often denoted

10. It is clearly essential to the proper choice of a
unit that it should be a constant quantity; hence we must
shew that the Radian is a constant angle. This we shall
do in the following articles.
11. Theorem. The length of the circumference of a
circle always bears a constant ratio to its diameter.

Take any two circles whose common centre is O.
the large circle inscribe a regular
polygon of n sides, ABCD....
Let OA, OB, OC,... meet the
smaller circle in the points a, b,
c, d... and join ab, be, cd,.... (
Then, by Euc. VI. 2, abed... is
a regular polygon of n sides inscribed in the smaller circle.
Since Oa = Ob, and OA = OB,

In
C
_ A