TI-58/TI-59 Week: Law of Cosines

TI-58/TI-59 Week:  Law of Cosines

Introduction

[ A ]:  stores either the angle θ or a 

[ B ]:  stores the length of side b

[ C ]:  stores the length of side c

[ D ]:  calculates the length of side a:

a^2 = b^2 + c^2 - 2 * b * c * cos θ

[ E ]:  calculates the angle θ

cos θ = (b^2 + c^2 - a^2) / (2 * b * c)

The angle θ is opposite slot of side a.

Program Listing

000 76 LBL

001 11 A

002 42 STO 

003 01 01

004 92 INV SBR (RTN)

005 76 LBL

006 12 B

007 42 STO

008 02 02

009 92 INV SBR

010 76 LBL

011 13 C

012 42 STO

013 03 03

014 92 INV SBR

015 76 LBL

016 14 D

017 43 RCL

018 02 02

019 33 x^2

020 85 +

021 43 RCL

022 03 03

023 33 x^2

024 75 -

025 02 2

026 65 ×

027 43 RCL

028 02 02

029 65 ×

030 43 RCL

031 03 03

032 65 ×

033 43 RCL

034 01 01

035 39 cos

036 95 =

037 34 √

038 42 STO 

039 04 04

040 INV SBR

041 76 LBL

042 15 E

043 53 (

044 43 RCL

045 02 02

046 33 x^2

047 85 +

048 43 RCL

049 03 03

050 33 x^2

051 75 -

052 43 RCL 

053 01 01

054 33 x^2

055 54 )

056 55 ÷

057 53 (

058 02 2

059 65 ×

060 43 RCL

061 02 02

062 65 ×

063 43 RCL

064 03 03

065 54 )

066 95 =

067 02 INV

068 39 cos  (arccos)

069 42 STO 

070 04 04

071 92 INV SBR

Examples

Calculating a:

Set the TI-58/TI-59 to Degrees mode:

Input:

50° [ A ]

45  [ B ]  (b)

35 [ C ] (c)

[ D ] returns a:  35.00312885

85° [ A ]

100  [ B ]  (b)

70 [ C ] (c)

[ D ] returns a:  116.9607609

Calculating θ:

52 [ A ]  (a)

38 [ B ] (b)

49 [ C ] (c)

[ E ] returns θ:  72.15813198

80 [ A ]  (a)

60 [ B ] (b)

65 [ C ] (c)

[ E ] returns θ:  79.47338145

Note:  The next post will be on July 23, 2022.

Eddie

All original content copyright, © 2011-2022.  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. 

TI-58/TI-59 Week: Hyperbolic Functions

 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

All original content copyright, © 2011-2022.  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. 

TI-58/TI-59 Week: Adding Machine

TI-58/TI-59 Week:  Adding Machine

Introduction

Turn your TI-58 and TI-59 into an adding machine, which uses register R00 as the accumulator. 

The soft keys do the following functions:

[ A ]:  Clear the accumulator

[ B ]:  Add [ + ]

[ +/- ] B:  Subtract [ - ]

[ C ]:  Multiply [ × ]

[ 1/x  ] [ C ]:  Divide [ ÷ ]

[ D ]:  Add % 

[ E ]:  Recall the accumulator

Program Listing

000 76 LBL

001 11 A

002 00 0

003 42 STO

004 00 00

005 92 INV SBR (RTN)

006 76 LBL

007 12 B

008 44 SUM

009 00 00

010 61 GTO

011 15 E

012 76 LBL

013 13 C

014 49 Prd

015 00 00

016 61 GTO

017 15 E

018 76 LBL

019 14 D

020 55 ÷

021 01 1

022 00 0

023 00 0

024 65 ×

025 43 RCL

026 00 00

027 95 =

028 44 SUM

029 00 00

030 61 GTO

031 15 E

032 76 LBL

033 15 E

034 43 RCL

035 00 00

036 92 INV SBR (RTN)

Example

Clear the Register:  [ A ]

Add 15:  15 [ B ]   (Result:  15)

Add 30:  30 [ B ]   (Result:  45)

Triple:  3 [ C ]   (Result:  135)

20% Discount:  20 [ +/- ] [ D ]  (Result:  108)

Halve:  2 [ 1/x ] [ C ] (Result:  54)

Subtract 30:  30 [ +/- ] [ B ]  (Result:  24)

Add 50%:  50 [ D ]  (Result: 36)

Recall the register:  [ E ]  (Result:  36)

Enjoy the accumulator.  

Eddie

All original content copyright, © 2011-2022.  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. 

TI-58/TI-59 Week: Numerical Derivative

TI-58/TI-59 Week:  Numerical Derivative

Introduction

The program estimates the numeric derivative:

d/dx f(x) = (f(x + h) - f(x)) / h

Registers used:

R01:  x

R02:  h

R03:  d/dx

Labels:

[ A ]:  store x

[ B ]:  store h

[ C ]:  calculate derivative

LBL E:  store f(x), assume x is in the display.  You can use registers R00 and R06 and above for registers.  Use Rad  ( [ 2nd ] [ - ] ) if f(x) contains trigonometric functions.  End each function with the steps =, INV SBR (RTN)

Function Listings

(step number, key code, key)

000 76 LBL

001 11 A

002 42 STO

003 01 01

004 92 INV SBR (RTN)

005 76 LBL

006 12 B

007 42 STO

008 02 02

009 92 INV SBR (RTN)

010 76 LBL

011 13 C

012 43 RCL

013 01 01

014 85 +

016 43 RCL

017 02 02

018 71 SBR

019 15 E

020 42 STO

021 03 03

022 43 RCL

023 01 01

024 71 SBR

025 15 E

026 94 +/-

027 85 +

028 43 RCL

029 03 03

030 95 =

031 55 ÷

032 43 RCL

033 02 02

034 95 =

035 42 STO

036 03 03

037 92 INV SBR (RTN)

038 76 LBL

039 15 E

...      .... ....

n-1 95 =

nnn 92 INV SBR (RTN)

Examples

f(x) = sin x;    Rad, sin

x = 0.5, h = 0.1, [ C ] returns 0.8521693479

x = 0.5, h = 1E-8, [ C ] returns 0.87755

f(x) = (1 + cos x)^1.5;   Rad, cos, +, 1, =, y^x, 1.5

x = 2, h = 0.01, [ C ] returns -1.035743295

x = 2, h = 1E-8, [ C ] returns -1.04206

f(x) = x * e^(x);   STO, 00, e^x * RCL, 00

x = 3, h = 0.01, [ C ] returns 80.84630054

x = 3, h = 1E-5, [ C ] returns 80.342648

Eddie

All original content copyright, © 2011-2022.  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. 

TI-58/TI-59 Week: ML 13 Curve Solution

 TI-58/TI-59 Week:  ML 13 Curve Solution

Introduction

Today's blog entry highlights just one of the wonderful programs offered by Texas Instrument's Master Library.  

When the Master Library ROM program module is in the TI-58, TI-58C (for this week I will say the TI-58 to refer to both the TI-58 and TI-58C), and the TI-59, call up the Curve Solution by pressing [ 2nd ] [ LRN ] (Pgm) 13.  

The user keys are assigned as:

A:  enter the central angle in radians ( θ )

B:  enter the circle's radius ( r )

C:  enter the arc length ( s )

D:  enter the chord length ( c )

E:  solve for the sector area ( A' )

A':  solve for the central angle ( θ' )

B':  solve for the radius ( r' )

C':  solve for arc length ( s' )

D':  solve for the chord length ( c' )

E':  solve for segment area ( a' )

Enter two of the variables θ, r, s, and c and solve for the rest, and at least one of the two variables θ or r must be entered.  

Examples

Example 1:  Known: r and c

r = 10.8

c = 12.0

[ 2nd ] (Pgm) 13

10.8 [ B ]  ( r )

12.0 [ D ]  ( c )

[ 2nd ] (A'):  1.17806194 rad  ( θ )

[ 2nd ] (C'):  12.72306896  (arc length)

[ E ]:  68.70457237 (sector area)

[ 2nd ] (E'):  14.824706 (segment area)

Example 2:  Known: θ and s

[ 2nd ] (Pgm) 13 

30° angle:   30 [ ÷ ] 180 [ × ] [ 2nd ]  ( π ) [ = ] [ A ]   ( θ )

40 [ C ]  ( s )

[ 2nd ] ( B' ):  76.39437268 ( r )

[ 2nd ] ( D' ): 39.54463718 ( c )

[ E ]:  1527.887454 (sector area)

[ 2nd ] (E'):  68.86240923 (segment area)

A little detour from our usually programming the calculator ourselves, but it is sometimes more effective and efficient to take advantage of either advanced built in or mainstream modules.  Alas, we do return to programming next time,

Eddie 

All original content copyright, © 2011-2022.  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. 

Fun With the TI-59

Fun With the TI-59

The following programs can be used on the TI-58C, TI-58, TI-59, TI-66, and any applicable emulator such as the RCL 58, RCL 59, and TI-5x. 

Vieta's Formula

Given the roots α, β, and γ we can calculate the coefficients of the general cubic equation a*x^3 + b*x^2 + c*x + d = 0 by:

s1 =  α + β + γ
s2 = α * β + β * γ + α * γ
p = α * β * γ

And the coefficients are:

a = 1
b = -s1
c = s2
d = -s3

The program displays a, b, c, and d.

TI-59 Program Vieta's Formula

000 76 LBL
001 11 A
002 42 STO
003 01 01
004 91 R/S
005 76 LBL
006 12 B
007 42 STO
008 02 02
009 91 R/S
010 76 LBL
011 13 C
012 42 STO
013 03 03
014 91 R/S
015 76 LBL
016 15 E
017 01 1
018 42 STO
019 04 04
020 91 R/S
021 43 RCL
022 01 01
023 85 +
024 43 RCL
025 02 02
026 85 +
027 43 RCL
028 03 03
029 95 =
030 94 +/-
031 42 STO
032 05 05
033 91 R/S
034 43 RCL
035 01 01
036 65 *
037 53 (
038 43 RCL
039 02 02
040 85 +
041 43 RCL
042 03 03
043 54 )
044 85 +
045 43 RCL
046 02 02
047 65 *
048 43 RCL
049 03 03
050 95 =
051 42 STO
052 06 06
053 91 R/S
054 43 RCL
055 01 01
056 65 *
057 43 RCL
058 02 02
059 65 *
060 43 RCL
061 03 03
062 95 =
063 94 +/-
064 42 STO
065 07 07
066 91 R/S

Example

Input:  α = 3, β = -5, γ = 6
Results: a = 1, b= -4, c = -27, d = 90

Random Numbers

Generate random numbers between 0 and 1 with this psuedorandom number generator.  You will need to enter a seed to start out.

Instructions:  enter a seed, [ RST ], [ R/S ].  Keep pressing [ R/S ] to generate additional random numbers.

TI-59 Program:  Psuedorandom Number Generator

000 85 +
001 89 PI
002 95 =
003 45 Y^X
004 05 5
005 95 =
006 22 INV
007 59 INT
008 91 R/S
009 81 RST

Source:  HP 25 Application Programs.  Hewlett Packard, 1975

Distance to the Horizon

This program computes the distance to an object, in nautical miles, given both the height of object (in feet) and height of the observer's eyes (in feet).

Formula:   

distance = 1.144 * ( √HE + √H )

Instructions.   Enter HE, [ RST ], [ R/S ], enter H, [ R/S ]

TI-59 Program: Distance to the Horizon

000 34 SQRT
001 85 +
002 91 R/S
003 34 SQRT
004 95 =
005 65 *
006 01 1
007 93 .
008 01 1
009 04 4
010 04 4
011 95 =
012 91 R/S
013 81 RST

Example

Input:  HE = 9.5 ft, H = 222 ft
Results:  20.57126091 n.m.

Source: 
"Distance To Or Beyond Horizon" (HAV 1-06A)  HP 65 Navigation Pac -1.  Hewlett Packard.  1974

Atmospheric Refraction

This program calculates atmospheric refraction of the light passing through the Earth's atmosphere given the apparent altitude of the light source, such as a star.

R = 1/(tan (h0 + 7.31/(h0 + 4.4)) 

The angle is in degrees.   Enter the apparent altitude, h0, in degrees, minutes, seconds format (DD.MMSSSS).  The result, R, is in arcminutes. 

000 60 DEG
001 88 DMS
002 42 STO
003 00 00
004 85 +
005 07 7
006 93 .
007 03 3
008 01 1
009 55 /
010 53 (
011 43 RCL
012 00 00
013 85 +
014 04 4
015 93 .
016 04 4
017 95 =
018 30 TAN
019 35 1/X
020 42 STO
021 01 01
022 91 R/S
023 81 RST

Example:

Input:  h0 = 43'24".  Enter as .4324
Result:  R = 26.63496931'

Source:
Meeus, Jean.  Astronomical Algorithms.  Willams-Bell Inc:  Richard, VA 1991 ISBN 0-943396-35-2

Head Winds and Cross Winds

The program calculates head winds and cross winds given :

* wind velocity (K)
* the direction wind from due north, clockwise, in degrees (D)
* the plane's heading direction angle from due north, clockwise, in degrees (D)
* any adjustment for the compass (V)

Head Wind: HW = K * cos(D - HDG - V)
Cross Wind:  RCW = K * sin(D - HDG - V)

Instructions:
Enter K, [ R/S ], enter D, [ R/S ], enter HDG, [ R/S ], enter V, [ R/S ]

Cross wind is displayed.  Press [ x<>t ] to get head wind.

Note:  As a program step, CP clears the t register. 

TI 59 Program:  Cross Winds and Head Winds

000 60 DEG
001 29 CP
002 32 X<->T
003 91 R/S
004 75 -
005 91 R/S
006 75 -
007 91 R/S
008 95 =
009 37 P->R
010 91 R/S
011 81 RST

Example

Input:
K = 25 mph
D  = 240 mph
HDG = 280 mph
V = 0

Results:
Cross Wind:  -16.09699024 mph [ x<>t ]
Head Wind:  19.1511108 mph

Source:
"Head Winds and Cross Winds"   HP 65 Aviation Pac 1.  Hewlett Packard, 1974

Eddie


All original content copyright, © 2011-2020.  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.

TI-59: Geometric Areas

TI-59: Geometric Areas

Introduction

The program calculates areas of planar geometric shapes.  The following user keys are defined:

A:  Enter A or radius.

B:  Enter B

C:  Enter C

D:  Display the total area

E:  Clear the total area

A':  Calculate the area of an Ellipse:  π*A*B.  For a circle, A = B

B':  Calculate the area of a Rectangle:  A*B.  For a square, A = B

C':  Calculate the area of a Triangle using Heron's Formula. 
S = (A + B + C)/2; √(S * (S - A) * (S - B) * (S - C))

D':  Calculate the area of Sector of a Circle:  π*B°*A^2/360
A:  radius, B: angle in degrees

E':  Calculate the area of a Regular Polygon:  (B * A^2)/(4 * tan(180°/B))
A:  length of a side, B:  number of sides (degrees)

Each calculation will add to the total area.

Memory Registers:

R01:  A
R02:  B
R03:  C
R04:  total area
R05:  S = (A + B + C)/2

The program is for the TI-58C, TI-58, TI-59, their emulators, and TI-66.

TI-59 Program:  Geometry Areas

000 76 LBL
001 11 A
002 42 STO
003 01 01
004 91 R/S
005 76 LBL
006 12 B
007 42 STO
008 02 02
009 91 R/S
010 76 LBL
011 13 C
012 42 STO
013 03 03
014 91 R/S
015 76 LBL
016 14 D
017 43 RCL
018 04 04
019 91 R/S
020 76 LBL
021 15 E
022 25 CLR
023 42 STO
024 04 04
025 91 R/S
026 76 LBL
027 16 A'
028 89 PI
029 65 *
030 43 RCL
031 01 01
032 65 *
033 43 RCL
034 02 02
035 95 =
036 44 SUM
037 04 04
038 91 R/S
039 76 LBL
040 17 B'
041 43 RCL
042 01 01
043 65 *
044 43 RCL
045 02 02
046 95 =
047 44 SUM
048 04 04
049 91 R/S
050 76 LBL
051 18 C'
052 53 (
053 43 RCL
054 01 01
055 85 +
056 43 RCL
057 02 02
058 85 +
059 43 RCL
060 03 03
061 54 )
062 55 /
063 02 2
064 95 =
065 42 STO
066 05 05
067 65 *
068 53 (
069 43 RCL
070 05 05
071 75 -
072 43 RCL
073 01 01
074 54 )
075 65 *
076 53 (
077 43 RCL
078 05 05
079 75 -
080 43 RCL
081 02 02
082 54 )
083 65 *
084 53 (
085 43 RCL
086 05 05
087 75 -
088 43 RCL
089 03 03
090 54 )
091 95 =
092 34 SQRT
093 44 SUM
094 04 04
095 91 R/S
096 76 LBL
097 19 D'
098 60 DEG
099 89 PI
100 65 *
101 43 RCL
102 02 02
103 65 *
104 43 RCL
105 01 01
106 33 X²
107 55 /
108 03 3
109 06 6
110 00 0
111 95 =
112 44 SUM
113 04 04
114 91 R/S
115 76 LBL
116 10 E'
117 53 (
118 01 1
119 08 8
120 00 0
121 55 /
122 43 RCL
123 02 02
124 54 )
125 60 DEG
126 30 TAN
127 65 *
128 04 4
129 95 =
130 35 1/X
131 65 *
132 43 RCL
133 02 02
134 65 *
135 43 RCL
136 01 01
137 33 X²
138 95 =
139 44 SUM
140 04 04
141 91 R/S

Example

5 [ A ]  6 [  B ]

[2nd] [ A' ]   Result:  94.24777961  (area of an ellipse with A = 5, B = 6)

[2nd] [ B' ]  Result:  30  (area of a rectangle with A = 5, B = 6)

9 [ C ]

[2nd] [ C' ]  Result: 14.14213562  (area of a triangle with A = 5, B = 6, C = 9)

9 [ A ] 60 [ B ]

[2nd] [ D' ]  Result: 42.41150082 (area of a circular sector A = 9, B = 60°)

9 [ A ] 8 [ B ]

[2nd] [ E' ]  Result:  391.1025971 (area of a polygon with a side length of 9 and 8 sides)

[ D ]  Total Area:  571.9040132

[ E ] clears total area

Eddie

All original content copyright, © 2011-2020.  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.

Retro Review: Texas Instruments TI-66

Retro Review:  Texas Instruments TI-66

Quick Facts

Company:  Texas Instruments
Years in Production: 1982 to 1985
Original Price: I estimate the original price to be from $70 to $100
Battery:  2 x LR44 or 2 x AR76
Type:  Scientific, Keystroke Programmable
Operating System: AOS
Number of Digits: 10
Memory:  512 steps, which can be allocated to a maximum of 64 memory registers
Accessories: Carrying Case, PC-200 Printer

I paid $7.99 at a Goodwill in Cerritos, CA.  The calculator came with the carrying case, User Guide, and Quick Start Guide, all boxed up.  What a lucky find!

The Next Generation of TI-58C

The TI-66 was slated to be the next generation of the TI-58C of 1978.  Virtually the keyboard design and commands of the TI-58C are present in the TI-66, but there are some differences:

*  The TI-66 is an landscape form with a gray keyboard, where as the TI-58C (and the related TI-58 and TI-59 has a black keyboard).

*  The TI-66 lacks a card reader.

*  The TI-66 also lacked a slot for modules. 

*  However, the TI-66 runs on coin batteries (AR76 or LR44), which can be found easily.  The TI-58C family had rechargeable battery packs, which cannot be easily purchased (few vendors sell them online).

*  In learn mode, when a step is registered, the TI-66 displays the key you just pressed with its mnemonic. 

Programming With The TI-66

Keystroke programming is fairly simple with the TI-66.  As I mentioned before, the TI-66 displays a mnemonic when a key stroke is registered (think HP 42S, HP 41C, or HP 32SII).  Examples are:

[ x^2 ] displays x↑2
[ π ] displays PI
[ Σ+ ] displays Σ+
[ √x ] displays √x

However, when it comes to programming the TI-66, patience is key!  The TI-66 takes on average, 1.5 seconds to register a new keystroke in learn (LRN) mode.  This is not for the speedy programmers among us.  This is my down point about the calculator, but it is not a deal breaker.

Other Programming Features

*  User labels A, B, C, D, and E; along A', B', C', D', and E'.  There are five keys dedicated to user labels.

*  Local labels have an unusual scheme.  They are defined by (almost) any key that is not a numeric key.  Therefore, we have labels such as 1/x, sin, and ÷.   This is carries over from the 1970s TI programmables (TI-57, TI-58, TI-58C, and TI-59). 

* 10 user flags: 0-9.

*  Indirect addressing

*  Storage arithmetic:  SUM (STO+), INV SUM (STO-), Prd (STO*), INV Prd (STO÷)

*  Comparisons:  compare the value in the display with register t.  Store amounts in register t with [ x<> t ].  Example:  a [ x<>t ] b [ 2nd ] (x≥t) tests whether b ≥ a).

*  An [ OP ] key gives access to additional functions and printing commands. 

A Partial List of OP Commands

OP 01 - 08 deal with printing, while 09 is not a valid code.

OP 10:  sign(x)
OP 11:  variance(x), variance(y)
OP 12:  slope, intercept  (linear regression)
OP 13:  correlation (linear regression)
OP 14:  x'  (predict x, linear regression)
OP 15:  y' (predict y, linear regression)

OP 2#:  increase register R0# (0-9) by 1
OP 3#:  decrease register R0# (0-9) by 1

Keyboard

Other than registering new programming commands, the keys are immediately responsive.  The keys are nice to the touch. 

Verdict

I would recommend the TI-66, especially if you want a TI-58, TI-58C, or TI-59, but don't want to deal with 1970s rechargeable batteries, or you are on a budget.  It is a very nice, feature rich calculator to have. 

Eddie

All original content copyright, © 2011-2019.  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.

HP Prime, HP 41C, TI-58C: Round to the Nearest 1/n

HP Prime, HP 41C, TI-58C:  Round to the Nearest 1/n

Introduction

The program RNEAR rounds a number x to the nearest 1/n.  For example, to round x to the nearest 10th, n = 10.  To round to the nearest 16th, n = 16.

HP Prime Program RNEAR

EXPORT RNEAR(x,n)

BEGIN

// round x to the nearest nth

// 2018-04-07 EWS

RETURN ROUND(FP(x)*n,0)/n+IP(x);

END;

HP 41C and Swiss Micros SM41 Program RNEAR

Keystrokes:  x [ENTER] y [XEQ] [ALPHA] RNEAR [ALPHA]

01 LBL^T REAR

02 FIX 0

03 STO 01

04 X<>Y

05 STO 02

06 RFC

07 *

08 RND

09 RCL 01

10 /

11 RCL 02

12 INT

13 +

14 FIX 4

15 RTN

TI-58C/TI-59 Program RNEAR

Store x into register 01

Store n into register 02

The result is stored in register 03

Minimum Registers Needed: 4 (I always leave register 00 for general use)

There is no rounding function on the TI-58C and TI-59, hence the rounding routine needs to be manually entered.

Step	Key Code	Key	Notes
000	43	RCL
001	01	01
002	22	INV
003	59	Int	INV Int: Frac
004	65	*
005	43	RCL
006	02	02
007	95	=
008	42	STO
009	03	03
010	00	0
011	93	.
012	05	5
013	32	x<>t	Store 0.5 to t
014	43	RCL
015	03	03
016	22	INV
017	59	Int
018	77	x≥t
019	55	[÷]	If frac(R03)≥0.5, go to label “÷”
020	76	Lbl
021	65	[*]	Label “×”
022	43	RCL
023	03	03
024	59	Int
025	55	÷
026	43	RCL
027	02	02
028	85	+
029	43	RCL
030	01	01
031	59	Int
032	95	=
033	42	STO
034	03	03
035	91	R/S	Display result
036	81	RST	End program
037	76	Lbl
038	55	[÷]	Label “÷”
039	01	1
040	44	SUM
041	03	03
042	61	GTO
043	65	[*]

Examples:

x = π

n = 10, result:  3.10 (nearest 10th)

n = 1000, result: 3.142 (nearest 1000th)

n = 16, result:  3.125 (nearest 16th)

Eddie

All original content copyright, © 2011-2018.  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.  Please contact the author if you have questions.