- } into a
hyperbolic identity, by
expanding it
completely in
terms of
integral powers of
sines and
cosines,
changing sine to sinh and
cosine to cosh, and...
- {\displaystyle \operatorname {Si} (ix)=i\operatorname {Shi} (x).} The
hyperbolic cosine integral is Chi(x)=γ+lnx+∫0xcosht−1tdt for |Arg(x)|<π ,{\displaystyle...
-
common use:
inverse hyperbolic sine,
inverse hyperbolic cosine,
inverse hyperbolic tangent,
inverse hyperbolic cosecant,
inverse hyperbolic secant, and inverse...
- {cosh(adjacent)}}={\frac {\cos B}{\sin A}}}. The
hyperbolic cosine of the
hypotenuse is the
product of the
hyperbolic cosines of the legs. cosh(hypotenuse)=cosh(a...
- In
hyperbolic geometry, the "law of
cosines" is a pair of
theorems relating the
sides and
angles of
triangles on a
hyperbolic plane,
analogous to the planar...
- trigonometry, the law of
cosines (also
known as the
cosine formula or
cosine rule)
relates the
lengths of the
sides of a
triangle to the
cosine of one of its angles...
-
where cosh is the
hyperbolic cosine. This
formula is a
special form of the
hyperbolic law of
cosines that
applies to all
hyperbolic triangles: cosh ...
- x} and y {\displaystyle y} , sine and
cosine can be
expressed in
terms of real sines,
cosines, and
hyperbolic functions as sin z = sin x cosh y...
-
indefinite integrals (antiderivatives) of
expressions involving the
inverse hyperbolic functions. For a
complete list of
integral formulas, see
lists of integrals...
- the
Chebyshev cube root. More precisely, the
values involving cosines and
hyperbolic cosines define, when p = −3, the same
analytic function denoted C1/3(q)...
