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.
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.