Plane trigonometry, by S.L. Loney.

330

TRIGONOMETRY.

281. There is no series, proceeding according to a
simple law, for the expansion of tan 0 in terms of 0,
similar to those of Arts. 279 and 280.
We shall find the series for tan 0 as far as the term
involving 05.
03 05
sin 3 0
For tan 0 =co 62 4
cos 0 6 - 2 4
2 +4
=( - -- -.. 1 - 2- + )
=(~-6+1~o 0- )Ll+(2-2~4+ )
t0- -0 + - )...-',1
) Fi0 2 24 )
_ =0~ ~ ~02 0+ + 2
+( 24..... J..
by the Binomial Theorem,
beomes very cumbrous and troublesome. 1
o- 6+120 -... 1+ 2- 24... +4.
neglecting 06 and higher powers of 0,
a was equal to 2the number of radians in the angle con- + -+ 0K
on reduction and neglecting powers of 0 above 05.
A similar method would give the series for tan 0 to
as many terms as we please. The method however soon
becomes very cumbrous and troublesome.
282. In Arts. 279 and 280 we tacitly assumed that
a was equal to the number of radians in the angle con