HP 12C: Hyperbolic Sine and Cosine, and their Inverses
Introduction
The following program calculates four hyperbolic functions:
sinh x = (e^x – e^(-x)) / 2
cosh x = (e^x + e^(-x)) / 2
arcsinh x = ln(x + √(x^2 + 1))
arccosh x = ln(x + √(x^2 - 1)) (principal arccosh x)
HP 12C Program: sinh x, cosh x, arcsinh x, arccosh x
Step #: Step Code: [ keys ]
# sinh x: GTO 01, R/S
01: __, 43, 22: [ g ] e^x
02: __, 43, 36: [ g ] LST x
03: __, __, 16: [ CHS ]
04: __, 43, 22: [ g ] e^x
05: __, __, 30: [ - ]
06: __, __, _2: [ 2 ]
07: __, __, 10: [ ÷ ]
08: 43, 33, 00: [ g ] GTO 00
# cosh x: GTO 09, R/S
09: __, 43, 22: [ g ] e^x
10: __, 43, 36: [ g ] LST x
11: __, __, 16: [ CHS ]
12: __, 43, 22: [ g ] e^x
13: __, __, 40: [ + ]
14: __, __, _2: [ 2 ]
15: __, __, 10: [ ÷ ]
16: 43, 33, 00: [ g ] GTO 00
# arcsinh x: GTO 17, R/S
17: __, __, 36: [ ENTER ]
18: __, __, 36: [ ENTER ]
19: __, __, _2: [ 2 ]
20: __, __, 21: [ y^x ]
21: __, __, _1: [ 1 ]
22: __, __, 40: [ + ]
23: __, 43, 21: [ √ ]
24: __, __, 40: [ + ]
25: __, 43, 23: [ g ] LN
26: 43, 33, 00: [ g ] GTO 00
# arccosh x: GTO 27 R/S
27: __, __, 36: [ ENTER ]
28: __, __, 36: [ ENTER ]
29: __, __, _2: [ 2 ]
30: __, __, 21: [ y^x ]
31: __, __, _1: [ 1 ]
32: __, __, 30: [ - ]
33: __, 43, 21: [ √ ]
34: __, __, 40: [ + ]
35: __, 43, 23: [ g ] LN
36: 43, 33, 00: [ g ] GTO 00
Instructions
1. Enter x
2. To calculate, press [ g ] GTO ##, then press [ R/S ].
* GTO 01 R/S: sinh x
* GTO 09 R/S: cosh x
* GTO 17 R/S: arcsinh x
* GTO 27 R/S: arccosh x
Examples
(Fix 4)
x |
sinh x |
cosh x |
-0.64 |
-0.6846 |
1.2119 |
0.59 |
0.6248 |
1.1792 |
1.23 |
1.5645 |
1.8568 |
3.74 |
21.0371 |
21.0609 |
Note: arccosh(1.2119) returns 0.64
Source
Selby, Samuel M. Ph. D. Sc. D. CRC Standard Mathematics Tables: Nineteenth Edition. The Chemical Rubber Co. Cleveland, OH. 1971. pp. 202, 211
Until next time,
Eddie
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