Acos2S; Acosh - HP 48gII Advanced User's Reference Manual

ACOS2S

CAS: Transform expressions replacing acos(x) with /2–asin(x).

ACOSH

Type: Analytic Function
Description: Inverse Hyperbolic Cosine Analytic Function: Returns the inverse hyperbolic cosine of the
argument.
For real arguments x < 1, ACOSH returns the complex result obtained for the argument (x, 0).
The inverse of ACOSH is a relation, not a function, since COSH sends more than one argument
to the same result. The inverse relation for COSH is expressed by ISOL as the general solution:
The function ACOSH is the inverse of a part of COSH, a part defined by restricting the domain
of COSH such that:
• each argument is sent to a distinct result, and
• each possible result is achieved.
The points in this restricted domain of COSH are called the principal values of the inverse relation.
ACOSH in its entirety is called the principal branch of the inverse relation, and the points sent by
ACOSH to the boundary of the restricted domain of COSH form the branch cuts of ACOSH.
The principal branch used by the hp49g+/hp48gII for ACOSH was chosen because it is
analytic in the regions where the arguments of the real-valued inverse function are defined. The
branch cut for the complex-valued hyperbolic arc cosine function occurs where the
corresponding real-valued function is undefined. The principal branch also preserves most of the
important symmetries.
The graphs below show the domain and range of ACOSH. The graph of the domain shows
where the branch cut occurs: the heavy solid line marks one side of the cut, while the feathered
3-6 Full Command and Function Reference
s1*ACOSH(Z)+2* *i*n1