Plane trigonometry, by S.L. Loney.

164

TRIGONOMETRY.

154. The inverse question, to find the angle, when
one of its trigonometrical ratios is given, will now be
easy.
Ex. Find the angle whose cotangent is 1-4109325, having given
cot 35~ 19' =14114799, and cot 35~ 20'= 14106098.
Let the required angle be 35~ 19' +x,
so that cot (35~ 19' + x) = 1-4109325.
From these three equations we have
For an increase of 60" in the angle a decrease of -0008701 in the cotangent,,, x"..,, -, 0005474. x: 60:: 5474: 8701, so that x=37-7.
Hence the required angle= 35019' 37'7".
155. In working all questions involving the application of the Principle of Proportional Parts the student must
be very careful to note whether the trigonometrical ratios
increase or decrease as the angle increases. As a help to
his memory he may observe that in the first quadrant the
3 trigonometrical ratios whose names begin with co-, i.e.
the cosine, the cotangent, and the cosecant, all decrease as
the angle increases.
Tables of logarithmic sines, cosines, etc.
156. In many kinds of trigonometric calculation, as
in the solution of triangles, we often require the logarithms
of trigonometrical ratios. To avoid the inconvenience of
first finding the sine of any angle from the tables and
then obtaining the logarithm of this sine by a second
application of the tables, it has been found desirable to
have separate tables giving the logarithms of the various