Thursday, August 18, 2016

TI-34 II, TI-34 Multiview, TI-36X Pro: Stored Operations and Recurring Sequences

TI-34 II, TI-34 Multiview, TI-36X Pro: Stored Operations and Recurring Sequences

Although not known as programming calculators, we can program small macros on the Texas Instruments TI-34 II, TI-34 Multiview, and TI-36X Pro calculators through the stored operation feature. You can store up to two operations on the TI-34 II and TI-34 Multiview, while only one operation can be stored on the TI-36X Pro.   The elementary calculator TI-15 also has this feature.

Executing the stored operation types whatever is stored.  For example if op=+11, then pressing 12 [op]* shows 12+11 on the screen.

There are limits to what can be programmed with this operation:

1.  For functions f(X), X is assumed to be entered, as once the operation is executed, what is stored is typed out.
2. There are no loops or IF-THEN-ELSE structures, hence the extent of the the stored operation is meant for quick calculations. I believe there is a 40 character limit.
3. For certain operations, you may need to enter certain functions or left hand parenthesis before executing the operation.
4. With the last answer command (Ans), we can program recurring sequences with one initial condition.  We will discuss this later.

General Steps for the TI-34 II and TI-34 Multiview:

1.  Press [2nd] [OP1] (set op1, >OP1) to edit your macro.  Press [Clear] if necessary.
2. When done, press [ENTER]

The steps are similar for OP2.

General steps for the TI-36X Pro (TI-30X Pro Multiview if you are outside the United States):

1.  Press [2nd] [ * ] (set op) to edit your macro.  Press [Clear] if necessary.
2. When done, press [ENTER]
3. Enter your variable, press [2nd] [ ) ] (op). The calculation is automatically made.

For the TI-15, the [OP1]/[OP2] has required repeated presses.  First for the edit mode, second to store the operation, subsequent presses execute the operation.  The TI-15 may have limited application, as in one step arithmetic macros.  I don't know if more complex macros can be programmed for the TI-15, since I do not own one.  For this post, I will focus on the TI-34 II, TI-34 Multiview, and TI-36X Pro.

Let's go over a few examples.

Example 1: Area of a circle.

The area of the circle is A = π * r^2.  Assume r will be in the display.

Set up the operation.  Press [2nd], (set op 1/2)*, [x^2], [ * ], [ π ].  The screen will read:

op=²*π, op1=²*π, or op2=²*π

Don't freak at this display, it is correct.  Press [ENTER].  Remember, this will be attached to the calculation whenever the stored operation is executed.

*Refer to the instructions above for your particular calculator.

Now enter r, and then press {op} to calculate the area.

Test Data:
r = 0.76,  Result = 1.814583917
0.76 {op} (display should show 0.76² * π )

r = 9, Result = 81*π = 254.4690049

Example 2: Convert °C to °F. (Degrees Celsius to Fahrenheit)

Formula: °F = °C * 9/5 + 32

Stored operation:  op = * 9 ÷ 5 + 32

Execute this stored operation in the same way as the above example.

Test data:
32°C, result 89.6°F
24°C, result 75.2°F

Example 3: Hypotenuse of a Right Triangle

Calculate the hypotenuse of a right triangle where one side is 5 units and the other varies.  Formula:  √(x^2 + 5^2) = (x^2 + 5^2)^0.5

Here X is inside an operation, so we'll need to make some adjustments.  Store the operation as:

op = ² + 5² ) ^ 0.5

When executing the operation, we'll have to include the left parenthesis, then enter the number, then execute the operation ({op}).  Otherwise, a syntax error occurs.

Test data:
x = 3.   Press [ ( ], 3, {op}.   The display should read (3² + 5²)^0.5 for the result of 5.830951895.

x = 4.5. Result: 6.726812024.

Example 4:  Percent Change

This will illustrate the use of variable registers.  The TI-34 II has five variable registers (A-E), the TI-34 Multiview has seven (x,y,z,t,a,b,c), and the TI-36X Pro has eight (x,y,z,t,a,b,c,d).

For this example, I will use the variable x, but feel free to use which one you like.

Percent change:  (n - x)/x * 100
where n = new value, x = old value.
The stored operation will be:  op = - x) ÷ x * 100

To execute, store the old value in x, then press [ ( ], enter new value, then execute the operation.

Test Data:
New = 50, Old = 36

36 [STO>] x, [ ( ], 50, {op}.   Result: 38.88888889

New = 26, Old = 36. Result: -27.77777778

Recurring Sequences:  u(n) = f( u(n-1) )

The stored operation format will be slightly different.  The variable Ans (last answer) represents u(n-1).  We have more freedom with the expression since Ans is used.

Before execution the operation, enter the initial condition, press [ENTER] to store in Ans.  Press {op} and repeat as desired.

Example 5:

Recurring sequence:  u(n) = 3 * u(n-1) - 1 with the initial condition u(1) = 1.

Stored Operation:  op = 3 * Ans - 1

Find the next six terms.

1, [ENTER], {op}

The next six terms are 2, 5, 14, 41, 122, 365.

Hope you find the stored operation feature helpful.  Until next time,

Eddie

This blog is property of Edward Shore, 2016