Sunday, March 11, 2018

Fun with the Texas Instruments TI-60


Fun with the Texas Instruments TI-60

Notes:

1.  I like to have the user input all the values into the registers before running the program.  This way, we can save program steps because the calculator doesn’t have to stop to ask for inputs.  Also, you don’t have to change all the values for different problems.  Finally, R/S can be used for only output.

2.  I keep register 0 (R0) out so that the user can have at least one register to store immediate results in further calculations.  I list the minimum partition for each program.


Great Circle Distance (in miles)

Formula:
D = acos (sin ϕ1 * sin ϕ2 + cos ϕ1 * cos ϕ2 * cos (λ1 – λ2)) * 3959 * π/180

Note: for kilometers, replace 3959 with 6371.

Where:
ϕ1, ϕ2:  Latitude of locations 1, 2; north is positive, south is negative
λ1, λ2:  Longitude of locations 1, 2:  east is positive, west is negative

Store before running:
R1:  ϕ1 as a decimal (convert from DMS if necessary)
R2:  λ1
R3: ϕ2
R4: λ2
Set the TI-60 in degrees mode.

Program (41 steps) – 2nd Part 5:
PG
OP
Key
PG
OP
Key
00
71
RCL
21
04
4
01
01
1
22
54
)
02
32
SIN
23
33
COS
03
65
*
24
95
=
04
71
RCL
25
12
INV
05
03
3
26
33
[COS]  (COS^-1)
06
32
SIN
27
65
*
07
85
+
28
03
3
08
71
RCL
29
09
9
09
01
1
30
05
5
10
33
COS
31
09
9
11
65
*
32
65
*
12
71
RCL
33
91
π
13
03
3
34
55
÷
14
33
COS
35
01
1
15
65
*
36
08
8
16
53
(
37
00
0
17
71
RCL
38
95
=
18
02
2
39
13
R/S
19
75
-
40
22
RST
20
71
RCL




Example:

Los Angeles:  ϕ = 34°13’ = 34.21666667°, λ = -(118°15’) = -(118.25°)
London:  ϕ = 51°30’26” = 51.50722222°, λ = -(0°7’39”) = -(0.1275°)

Result:  5431.617778 mi

Tip: For DMS-DD conversions: if you have a negative angle, enter the angle without the negative sign, do the conversion DMS-DD, then press [ +/- ].

Impedance of a Series Resonance Circuit

This program gives both the magnitude and phase angle. 

Impedance:   Z = R + j*(ω*L – 1/(ω*C))
Where:  ω = 2*π*F
Magnitude:  abs(Z)
Phase Angle:  arg(Z)

Variables:
R = resistance ( Ω )
C = capacitor ( farads )
L = inductor ( henrys )
F = Frequency (Hz)

Store before running:
R1:  R
R2:  C
R3:  L
R4:  F
Set the TI-60 in degrees mode.

Program (35 steps) – 2nd Part 5:
PG
OP
Key
PG
OP
Key
00
02
2
18
02
2
01
65
*
19
54
)
02
91
π
20
76
1/x
03
65
*
21
95
=
04
71
RCL
22
61
STO
05
04
4
23
05
5
06
95
=
24
71
RCL
07
61
STO
25
01
1
08
05
5
26
52
X<>Y
09
65
*
27
71
RCL
10
71
RCL
28
05
5
11
03
3
29
12
INV
12
75
-
30
38
[P-R]
(R-P)
13
53
(
31
13
R/S
14
71
RCL
32
52
X<>Y
15
05
5
33
13
R/S
16
65
*
34
22
RST
17
71
RCL




Example:

Input:
R1:  R = 11.56 Ω
R2:  C = 0.0002 F
R3:  L =  0.018 H
R4:  F = 72 Hz

Results:
Phase Angle (θ) = -14.12679136°
Magnitude = 11.92049981

Linear Interpolation

Given points (x0, y0) and (x1, y1) with x0 < x < x1, we can estimate y by linear interpolation by:

y = ((x1 – x)*y0 + (x – x0)*y1)/(x1 – x0)

How good of an approximation depends on how close x0 and x1 are, and whether the curve that is being approximated is close to linear.

Store before running:
R1:  x1
R2:  y1
R3:  x2
R4:  y2
R5:  x

Program (34 steps) – 2nd Part 5:
PG
OP
Key
PG
OP
Key
00
53
(
17
01
1
01
53
(
18
54
)
02
71
RCL
19
65
*
03
03
3
20
71
RCL
04
75
-
21
04
4
05
71
RCL
22
54
)
06
05
5
23
55
÷
07
54
)
24
53
(
08
65
*
25
71
RCL
09
71
RCL
26
03
3
10
02
2
27
75
-
11
85
+
28
71
RCL
12
53
(
29
01
1
13
71
RCL
30
54
)
14
05
5
31
95
=
15
75
-
32
13
R/S
16
71
RCL
33
22
RST


Example:

Input:
R1:  x1 = 2
R2:  y1 = 3
R3:  x2 = 4
R4:  y2 = 8
R5:  x = 3

Result:
y = 5.5

Purchase of a Car:  How much can I afford?

The program will calculate the sticker price (price before sales tax) of an automobile that you can afford.  You give the term you want, the interest rate you qualify for, the sales tax rate, and the maximum payment you can afford.  This assumes that you don’t put any money down.

Formulas:
A = P/I * (1 – (1 + I)^-N) / (1 + S)

A = sticker price of the car
P = monthly payment
I = monthly interest rate of the loan, in decimal.   I = rate/1200
N = number of months.  N = years*12
S = sales tax rate, in decimal.  S = sales tax rate/100

Input:
R1:  number of payments
R2:  monthly interest rate
R3:  payment
R4:  sales tax rate, in decimal

Program (30 steps), 2nd Part 4:
PG
OP
Key
PG
OP
Key
00
71
RCL
15
45
y^x
01
03
3
16
71
RCL
02
55
÷
17
01
1
03
71
RCL
18
94
+/-
04
02
2
19
54
)
05
65
*
20
55
÷
06
53
(
21
53
(
07
01
1
22
01
1
08
75
-
23
85
+
09
53
(
24
71
RCL
10
01
1
25
04
4
11
85
+
26
54
)
12
71
RCL
27
95
=
13
02
2
28
13
R/S
14
54
)
29
22
RST

Example:

Input:
R1:  number of payments = 60, (5 year term)
R2:  monthly interest rate = 0.05/12 = 0.004166667, (5% annual interest rate)
R3:  payment = 400
R4:  sales tax rate, in decimal = 0.095, (9.5%)


Result:  19357.34

In this example, the highest sticker price that can be afforded is $19,357.34 (before sales tax).

I enjoy programming with the TI-60, unlike most Texas Instruments calculators that have keystroke programming, the TI-60 shows the step and key code you have entered instead of advancing to the next step with code 00. 

Eddie

This blog is property of Edward Shore, 2018.

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