Plane trigonometry, by S.L. Loney.

10

TRIGONOMETRY.

EXAMPLES. II.
1. If the radius of the earth be 4000 miles, what is the length of its
circumference?
2. The wheel of a railway carriage is 3 feet in diameter and makes
3 revolutions in a second; how fast is the train going?
3. A mill sail whose length is 18 feet makes 10 revolutions per
m inute. What distance does its end travel in an hour?
4. The diameter of a halfpenny is an inch; what is the length of a
piece of string which would just surround its curved edge?
5. Assuming that the earth describes in one year a circle, of
92500000 miles radius, whose centre is the sun, how many miles does the
earth travel in a year?
6. The radius of a carriage wheel is 1 ft. 9 ins., and it turns
through 80~ in 9th of a second; how many miles does the wheel travel in
9
one hour?
15. Theorem. The radian is a constant angle.
Take the figure of Art. 9. Let the arc AB be a
quadrant of the circle, i.e. one quarter of the circumference.
7r9r
By Art. 12, the length of AB is therefore 7, where r
is the radius of the circle.
By Euc. VI. 33, we know that angles at the centre of
any circle are to one another as the arcs on which they
stand.
zAOP arcAP r 2
Hence = =ce A OB arc AB wr 7r
2r
i.e. zAOP=2. zAOB.
7Bu
But we defined the angle AOP to be a Radian.