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
All original content copyright, © 2011-2024. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.