Hyperbolic SIN of a complex argument

Hyperbolic SIN of a complex argument

Postby jeff110264 » Sun Mar 29, 2015 2:13 am

This program computes SINH(Z) where Z is complex.
Argument entry: angle(Z) ENTER |Z| (so Y-reg = angle of Z in deg, X-reg = mag(Z))
Returns X-reg = mag(SINH(Z)) and Y-reg = angle of SINH(Z) in degrees.
The pgm changes registers 06,07,08,09, and the whole stack.

Implements Euler's definition of SINH(Z) = SINH(x + jy) = [(e^x * e^jy) - (e^-x * e^-jy)] / 2
and we say (e^x * e^jy) = a + jb, and (e^-x * e^-jy) = c + jd.

LBL SINHZ ; name of pgm
P-R ; get X=x
STO 06 ; save x
RDN
57.29578
* ; get y in degrees
STO 07
ENTER ; get Y-reg = y
RCL 06 ; get X-reg = x
e^x ; now X-reg = e^x
P-R ; now X-reg = a, Y-reg = b
STO 08 ; save a
RDN
STO 09 ; save b
RCL 07 ; get X-reg = y (still in degrees)
CHS ; we need (-y)
ENTER ; get it in Y-reg
RCL 06 ; get X-reg = x
CHS ; need (-x)
e^x ; get e^-x
P-R ; now X-reg = c, and Y-reg = d
CHS ; now X-reg = (-c)
RCL 08 ; get a
+ ; compute a-c
STO 06 ; save it
RDN ; now X-reg = d
CHS ; need (-d)
RCL 09 ; get b
+ ; compute b-d
STO 07 ; save it. Now just get the result in polar form
RCL 06 ; now Y-reg = (b-d) and X-reg = (a-b)
R-P ; convert to polar form
2 ; don't forget to divide the mag by 2!
/
END ; end with SINH(Z) magnitude in X-reg and angle (in deg) in Y-reg.
jeff110264
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