Plane trigonometry, by S.L. Loney.

.THE RADIAN.

11

Hence a Radian =. Z A OB
7,
2
=- x a right angle.
7r
Since a right angle is a constant angle and since we
have shewn (Art. 12) that r' is a constant quantity, it
follows that a Radian is a constant angle, and is therefore
the same whatever be the circle from which it is derived.
16. Magnitude of a Radian.
By the previous article a radian
2 180~
=- x a right angle = —
7r 7T~
314159265..= 57-29577950
3'14159265...
= 57~ 17' 448" nearly.
2
17. Since a Radian = - x a right angle,
mr
therefore a right angle =-. radians,
2'
so that 180= 2 right angles = wr radians,
and 360~= 4 right angles = 27r radians.
Hence when the revolving line (Art. 6) has made a
complete revolution it has described an angle equal to
27r radians; when it has made three complete revolutions
it has described an angle of Gr radians; when it has made
n revolutions it has described an angle of 2n7r radians.
18. In practice the symbol " c " is generally omitted
and instead of "an angle wrc" we find written "an
angle 7r."