Coshine

Should a shine or coshine be wanted which is not in the table, advantage may be taken of the differential of cosh x being sinh x, and vice versa. Thus, sinh x and cosh x being known, the shine or coshine of x + y, y being small compared to x, may be calculated from these relationships—[…]

Considering equation (8) in which ϵ = −1 we have a similar situation to our previous analysis in which the hyperbolic functions replace the trigonometric ones. However, this leads to significant changes in the results, e.g., if in equation (18) the cosines are replaced by coshines the equation has no solutions since coshines are always greater than or equal to one.

In (4) the function cos{h} denotes that either cosine or coshine functions are used depending upon whether the third charateristic^([sic]) root is real or imaginary.