Plane trigonometry, by S.L. Loney.

402

TRIGONOMETRY.

Hence 3-2010250079
- *0594323552
rT = 3-14159265/27
This is the value of 7r correct to 8 places of decimals.
By taking the first series to 21 terms and the second
series to three terms we should get 7r correct to sixteen
places.
349. Rutherford's Series. A further simplification
of Machin's formula is the expression
I 1 1 7r
4 tan-1 - tan-l + tan-' =
5 70 99 4'
For we have
1 1
1 1 _70 99 29
tan-' 7 -tan- 9 = tan- 70 99 = tan- 29
1 1 6931
+70'99
= tan-'1
239'
EXAMPLES. LIX.
Assuming that
1 1
0 - n7r=tan 0 - - tan3 0 + tan5 -...,
3 5
write down the value of n when 0 lies between
117r 137 77r 97r
1. 2. and 2 and
4 4 4 4
197r 217r 37r 57r
3, - and 4 ' 4, - - and --.
117r 137r
5. - - and- 4.
5.4