## 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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