Plane trigonometry, by S.L. Loney.

MEASUREMENT OF ANY ANGLE IN RADIANS.

15

Let AOP be the angle which has been descril
line starting from OA and revolving into the position OP.
With centre 0 and any radius
describe a circle cutting OA and
OP in the points A and P.
Let the angle A OB be a radian,
so that the arc AB is equal to the
radius OA.
By Euc. VI. 33, we have
z AOP z AOP arc AP arc AP
A Radian z AOB arc AB Radius '
so that z A OP a A Radian.
Radius
Hence the theorem is proved.

bed by a
a
A

22. Ex. 1. Find the angle subtended at the centre of a circle of
radius 3 feet by an arc of length 1 foot.
are 1
The number of radians in the angle = adiu- 3
radius 3
Hence the angle
1 12 2 600
= radian= -. right angle= x 900 = = 19~,
3 37 377 7r
22
taking ir equal to 22
7'
Ex. 2. In a circle of 5 feet radius what is the length of the arc which
subtends an angle of 33~ 15' at the centre?
If x feet be the required length, we have
-= number of radians in 33~ 15'
5
334
=180- (Art.19).
133
720
133 133 22.'. x- 144 r feet = 144 x feet nearly
= 2t, feet nearly.