Plane trigonometry, by S.L. Loney.

PROPORTIONAL PARTS.

167

Ex. 3. Given L sin 14~ 6' = 9 3867040
find L cosec 14~ 6'.
Here log sin 14~ 6' = L sin 14~ 6' - 10
= - 1 + 3867040.
Now log cosec 14~ 6' = log 14 6'
sin 14' 6'
= - log sin 14~ 6'
=1- 3867040 = '6132960.
Hence L cosec 14~ 6'= 10 6132960.
The error to be avoided is this; the student sometimes assumes that
because
log cosec 14 6' = - log sin 14~ 6',
he may therefore assume that
L cosec 14~ 6'= - L sin 14~ 6'.
This is obviously untrue.
EXAMPLES. XXIV.
1. Given log 35705 = 45527290
and log 35706 = 4-5527142,
find the values of log 35705-7 and log 35'70585.
2. Given log 5-8743 = 7689487
and log 587 44 = 2-7689561,
find the values of log 58743-57 and log -00587432.
3. Given log 47847=4-6798547
and log 47848 = 4-6798638,
find the numbers whose logarithms are respectively
2-6798593 and 3-6798617.