3-14 Full Command and Function Reference
Flags: Principal Solution (–1), Numerical Results (–3), Angle Mode (–17, –18)
Input/Output:
Level 1/Argument 1 Level 1/Item 1
z
→
asin z
'symb'
→
'ASIN(symb)'
See also: ACOS, ATAN, ISOL, SIN
ASIN2C
CAS: Transform expressions replacing asin(x) with π/2–acos(x).
ASIN2T
CAS: Transform expressions replacing asin(x) with atan(x/√(1-x^2))
ASINH
Type: Analytic Function
Description: Arc Hyperbolic Sine Analytic Function: Returns the inverse hyperbolic sine of the argument.
The inverse of SINH is a relation, not a function, since SINH sends more than one argument to
the same result. The inverse relation for SINH is expressed by ISOL as the general solution:
ASINH(Z)*(–1)^n1+π*i*n1
The function ASINH is the inverse of a part of SINH, a part defined by restricting the domain of
SINH such that:
• each argument is sent to a distinct result, and
• each possible result is achieved.
The points in this restricted domain of SINH are called the principal values of the inverse relation.
ASINH in its entirety is called the principal branch of the inverse relation, and the points sent by
ASINH to the boundary of the restricted domain of SINH form the branch cuts of ASINH.
The principal branch used by the hp49g+/hp48gII for ASINH was chosen because it is analytic
in the regions where the arguments of the real-valued function are defined. The branch cut for the
complex-valued ASINH function occurs where the corresponding real-valued function is
undefined. The principal branch also preserves most of the important symmetries.
The graph for ASINH can be found from the graph for ASIN (see ASIN) and the relationship
asinh z = –i asin iz.
Access: …Ñ
HYPERBOLIC ASINH (Ñ is the right-shift of the 8key).
Flags: Principal Solution (–1), Numerical Results (–3)
Input/Output:
Level 1/Argument 1 Level 1/Item 1
z
→
asinh z
'symb'
→
'ASINH(symb)'
See also: ACOSH, ATANH, ISOL, SINH
ASN
Type: Command
Description: Assign Command: Defines a single key on the user keyboard by assigning the given object to the
key x
key
, which is specified as rc.pf.
The argument x
key
is a real number rc.pf specifying the key by its row number r, column number c,
shift plane p and shift-and-hold flag f. A value of f=0 represents a normal shifted key assignment
(where the shift is released prior to pressing the key); whereby f=1 corresponds to a shift-and-
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