Plane trigonometry, by S.L. Loney.

THE RADIAN.

9

355
[N.B. The fraction — 3 may be remembered thus; write down the
first three odd numbers repeating each twice, thus 113355; divide the
number thus obtained into portions and let the first part be divided into
the second, thus 113) 355(.
The quotient is the value of 7r to 6 places of decimals.]
To sum up. An approximate value of 7r, correct
22
to 2 places of decimals, is the fraction 7; a more
accurate value is 3 14159....
By division we can shew that
1
- =3183098862....
7r
14. Ex. 1. The diameter of a tricycle wheel is 28 inches; through
what distance does its centre move during one revolution of the wheel?
The radius r is here 14 inches.
The circumference therefore = 2. r. 14 = 287r inches.
22 22
Taking r = -, the circumference = 28 x - inches= 7 ft. 4 inches approximately.
Giving 7r the more accurate value 3'14159265... the circumference
=28 x 3-14159265... inches = 7 ft. 3 96459... inches.
Ex. 2. What must be the radius of a circular running path, round
which an athlete must run 5 times in order to describe one mile?
1
The circumference must be - x 1760, i.e. 352, yards.
Hence, if r be the radius of the path in yards, we have 27r= 352,
176
i.e. r= - yards.
7r
22 176 x 7
Taking 7r= -, we have r= 22 =56 yards nearly.
Taking the more accurate value - = 31831, we have
r=176x 31831= 5602256 yards.
r= 176 x -31831 =56-02256 yards.