Plane trigonometry, by S.L. Loney.

34

TRIGONOMETRY.

IIMP /3a /3
Hence sin 60~= V =
OP 2a 2 '
OM a 1
cos 60= — =
OP 2a 2'
sin 60~
and tan 60~= = 0 /3.
cos 600
36. Angle of 0~.
Let' the revolving line OP have turned through a very
small angle, so that the angle
MOP is very small. P
The magnitude of MP is M A
then very small and initially,
before OP had turned through an angle big enough to be
perceived, the quantity MP was smaller than any quantity
we could assign, i.e. was what we denote by 0.
Also, in this case, the two points M and P very nearly
coincide, and the smaller the angle AOP the more nearly
do they coincide.
Hence, when the angle AOP is actually zero, the two
lengths 01M and OP are equal and MP is zero.
Hence sin 0O = M= 0,
OM OP
cos 0= -- - 1,
and tan 0~ = = 0.
Also cot 0~ = the value of mp when M and P coincide
MR
= the ratio of a finite quantity to something infinitely
small
= a quantity which is infinitely great.
Such a quantity is usually denoted by the symbol oo.