Plane trigonometry, by S.L. Loney.

262

TRIGONOMETRY.

Hence when 0 is very small the quantity sn.0 lies
between 1 and a quantity which differs from unity by an
indefinitely small quantity.
In other words, when 0 is made indefinitely small the
qatt si6sinO
quantity si 0, and therefore -, is ultimately equal to
unity, i.e. the smaller an angle becomes the more nearly
is its sine equal to the number of radians in it.
This is often shortly expressed thus;
sin 0 = 8, when 0 is very small.
So also tan 0 =, when 0 is very small.
Cor. Putting 0= -, it follows that, when 0 is indefinitely small, n is indefinitely great.. a
sin -
Hence -- is unity, when n is indefinitely great.
n
n
So n sin - = a, when n is indefinitely great.
229. In the preceding article it must be particularly
noticed that 0 is the number of radians in the angle
considered.
The value of sin a~, when a is small, may be found.
For, since 7rc = 180~, we have
a = v7r 180).
es a 180atic
by the result of the last article.180