Assume; Atan - HP 48gII Advanced User's Reference Manual

...ãL
Access:
Flags: Binary Integer Wordsize (–5 through –10), Binary Integer Base (–11, –12)
Input/Output:
See also: SL, SLB, SR, SRB

ASSUME

CAS: Place assumptions on variables treated by CAS as real when Complex mode is set.

ATAN

Type: Analytic Function
Description: Arc Tangent Analytic Function: Returns the value of the angle having the given tangent.
For a real argument, the result ranges from –90 to +90 degrees (– /2 to + /2 radians; –100 to
+100 grads).
The inverse of TAN is a relation, not a function, since TAN sends more than one argument to the
same result. The inverse relation for TAN is expressed by ISOL as the general solution:
The function ATAN is the inverse of a part of TAN, a part defined by restricting the domain of
TAN such that:
• each argument is sent to a distinct result, and
• each possible result is achieved.
The points in this restricted domain of TAN are called the principal values of the inverse relation.
ATAN in its entirety is called the principal branch of the inverse relation, and the points sent by
ATAN to the boundary of the restricted domain of TAN form the branch cuts of ATAN.
The principal branch used by the hp49g+/hp48gII for ATAN was chosen because it is analytic
in the regions where the arguments of the real-valued inverse function are defined. The branch
cuts for the complex-valued arc tangent function occur 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 ATAN. The graph of the domain shows where
the branch cuts occur: the heavy solid line marks one side of a cut, while the feathered lines mark
the other side of a cut. The graph of the range shows where each side of each cut is mapped
under the function.
These graphs show the inverse relation ATAN(Z)+ *n1 for the case n1 = 0. For other values of
n1, the vertical band in the lower graph is translated to the right (for n1 positive) or to the left
(for n1 negative). Together, the bands cover the whole complex plane, the domain of TAN.
View these graphs with domain and range reversed to see how the domain of TAN is restricted
to make an inverse function possible. Consider the vertical band in the lower graph as the
restricted domain Z = (x, y). TAN sends this domain onto the whole complex plane in the range
W = (u, v) = TAN(x, y) in the upper graph.
3-16 Full Command and Function Reference
BIT ASR
Level 1/Argument 1
#n
1
( ãis the right-shift of the 3key).
ATAN(Z)+ *n1
Level 1/Item 1
#n
2