Had the earth no obliquity, the effect would be as the squares of the cosines of the latitude; but the ratio is diminished by the inclination of the axis.
For the smallest angle, when the correction is a maximum, this correction will be about 20′ of latitude at the equator; for other latitudes it is diminished as the squares of the cosines of the latitude.
In other latitudes it is diminished in the ratio of the squares of the cosines of the latitude; it therefore becomes 1/434 in that latitude the square of whose sine is ⅓.
The first cases in which rational functions are expressed in sines and cosines were given by Euler (Subsidium calculi sinuum, Novi Comm.
On adding the expressions together we obtain a series of sines and cosines which represents [f](x) for the interval -l to l.
Also let e denote the extension in the direction of a line the direction cosines of which are l, m, n.
The sum of the squares of the cosines of the angles which a right line makes with three rectangular right lines is equal to unity.
Knowing the sines and the cosines of two arcs a and b, to find the sine and the cosine of their sum and of their difference.
The above list will hopefully give you a few useful examples demonstrating the appropriate usage of "cosines" in a variety of sentences. We hope that you will now be able to make sentences using this word.
