TI-58/TI-59 Week: Hyperbolic Functions
Introduction
The program listing sets up the soft keys as the following:
[ A ] : calculate sinh
sinh x = (e^x - 1/e^x) / 2
[ 2nd ] ( A' ): calculate arcsinh (principal branch)
arcsinh x = ln | x + √(x^2 + 1) |
[ B ]: calculate cosh
cosh x = (e^x + 1/e^x) / 2
[ 2nd ] ( B' ): calculate arccosh (principal branch)
arccosh x = ln | x + √(x^2 - 1) |
[ C ]: calculate tanh
tanh x = sinh x / cosh x = (e^x - e^(-x)) / (e^x + e^(-x))
[ 2nd ] ( C' ): calculate arctanh
arctanh x = ln | √((x^2 + 1) / (1 - x)) |
R00 is used in calculation. Note: INV ln x, e^x
Program Listing
000 76 LBL (sinh x)
001 11 A
002 53 (
003 22 INV
004 23 ln x
005 42 STO
006 00 00
007 75 -
008 43 RCL
009 00 00
010 35 1/x
011 54 )
012 55 ÷
013 02 2
014 95 =
015 92 INV SBR (RTN)
016 76 LBL (arcsinh x)
017 16 A'
018 42 STO
019 00 00
020 85 +
021 53 (
022 43 RCL
023 00 00
024 33 x^2
025 85 -
026 01 1
027 54 )
028 34 √
029 95 =
030 50 |x|
031 23 ln x
032 92 INV SBR
033 76 LBL (cosh x)
034 12 B
035 53 (
036 22 INV
037 23 ln x
038 42 STO
039 39 00
040 85 +
041 43 RCL
042 00 00
043 35 1/x
044 54 )
045 55 ÷
046 02 2
047 95 =
048 92 INV SBR
049 76 LBL (arccosh x)
050 17 B'
051 42 STO
052 00 00
053 85 +
054 53 (
055 43 RCL
056 00 00
057 33 x^2
058 75 -
059 01 1
060 54 )
061 34 √
062 95 =
063 50 |x|
064 23 ln x
065 92 INV SBR
066 76 LBL (tanh x)
067 13 C
068 53 (
069 22 INV
070 23 ln x
071 42 STO
072 00 00
073 75 -
074 43 RCL
075 00 00
076 35 1/x
077 54 )
078 55 ÷
079 53 (
080 43 RCL
081 00 00
082 85 +
083 43 RCL
084 00 00
085 35 1/x
086 54 )
087 95 =
088 92 INV SBR
089 76 LBL (arctahn x)
090 18 C'
091 53 (
092 42 STO
093 00 00
094 85 +
095 01 1
096 54 )
097 55 ÷
098 53 (
099 01 1
100 75 -
101 43 RCL
102 00 00
103 54 )
104 95 =
105 34 √
106 50 |x|
107 23 ln x
108 92 INV SBR
Examples
sinh 3.96; 3.96 [ A ] returns 26.21913142
arcsinh 40; 40 [ 2nd ] (A') returns 4.382182848
cosh -2.22; -2.22 [ B ] returns 4.657969987
arccosh 100: 100 [ 2nd ] (B') returns 5.298292366
tanh 0.58: 0.58 [ C ] returns 0.5226654297
arctanh 0.96: 0.96 [ 2nd ] (C') returns 1.94591014906
Eddie
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