Difference between revisions of "Calculator Tips"

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* 2/24/2024 update - the Casio fx-991EX has recently been discontinued in favor of the fx-991CW.  More soon on whether that will become the new recommended calculator or not.
+
* 3/7 Update: This page is now almost solely focused on the TI 84+ series of calculators (with a bit of a coda on TI-89).  For information on the old Casio fx-991EX series, see [[Calculator Tips/Classwiz]].
−
* 2/26/2024 update - the vast majority of respondents to a calculator survey for ECE 110 and EGR 224 indicate having a TI-84 Plus of some kind, so this page will be reorganized accordingly.
 
  
−
This page contains information about how to use various calculators for different classes.  
+
== TI 84-Plus (2024 Edition) ==
 +
The following guide was written while using a TI-84 Plus C Silver Edition.  There are subtle differences between this edition and other (TI-84 Plus CE, for example).  Anywhere "84+" shows up below refers specifically to the TI-84 Plus C Silver Edition.  As exceptions are noted, they will be posted. 
 +
 
 +
=== Using this guide ===
 +
When you are given keystrokes:
 +
* '''2ND-Something''' means hit the 2ND key and then a key that has a secondary command of Something.  For instance, 2ND-QUIT would mean hitting 2ND and then the key primarily labeled MODE, which has QUIT above it in the same color as the 2ND key
 +
* '''ALPHA-Letter''' means hit the ALPHA key and then a key that has a letter of Letter.  For instance, ALPHA-D would mean hitting ALPHA and then the key primarily labeled $$x^{-1}$$, which has D above it in the same color as the ALPHA key
 +
* '''MATH-CMPLX-Command(Number)''' means hit the MATH button to get to the MATH menu, then use the left/right arrow buttons to scroll over to the CMPLX submenu, then use the up/down arrow buttons to scroll down to the Command command.  Alternately, hit the MATH button to get to the MATH menu, then use the arrow buttons to scroll over to the CMPLX submenu, then type the Number related to the command you want.  For instance, MTH-CMPLX-angle(4) will get the calculator to type <code>angle(</code>
 +
* A '''/''' means use the ÷ key (÷ is annoying to type in Mediawiki)
 +
* A '''*''' means use the $$\times$$ key (same reason)
 +
 
 +
=== Initial Setup ===
 +
==== Modes ====
 +
[[File:TI84 complex settings.PNG|200px|thumb|right|Modes for doing complex calculations]]
 +
The default modes for the 84+ are not all useful for doing complex calculations.  For instance, if you try to take the square root of a negative number with a factory-reset 84+, you will get an error!  As a result, we recommend that you click the MODE button and then set the following modes before doing work:
 +
* SCI (for scientific notation)
 +
* FLOAT: 3 (to get three figures after the decimal; this yields four significant figures in scientific mode)
 +
* RADIAN (default; for some 84+, this '''must''' be in radians to work with complex exponentials)
 +
* re^(θi) to report using Euler notation - this will generally be the most useful as you will get a magnitude and a phase out of it
 +
Click 2ND-QUIT to get out of this menu
 +
 
 +
==== Helpful Constants ====
 +
[[File:TI84_save_use_D.PNG|200px|thumb|right|Saving and using a constant to convert from degrees to radians]]
 +
There will be times that you want to quickly convert a number from degrees to radians and vice versa.  Given the number of times you may need to use these conversion factors, it may be helpful to store one of them in the calculator.  Here is one recommendation:
 +
* Use letter D as the conversation from degrees to radians
 +
* Calculate $$\pi$$/180, then store it as D:
 +
** 2ND-PI, ÷, 180, STO>, ALPHA-D, ENTER
 +
* Use 1/D to convert from radians to degrees
 +
Now if you want to calculate $$10∠60^{\circ}$$ you can type $$10e^{i60D}$$ or $$10*e^{i*60*D}$$. 
 +
[[File:TI84_save_use_D_2.PNG|200px|thumb|right|Extracting an angle and using a constant to convert from radians to degrees]]
 +
If you need to get an angle in degrees from a complex number, you can use the
 +
angle() command in the MATH-CMPLX menu and then divide the result by D.  For instance, to determine the angle in degrees of $$4+j5$$:
 +
* Find $$4+j5$$ using the 84+
 +
** 4, +, 2ND-i, 5, ENTER
 +
*** Looks like <code>4+i5</code>
 +
*** reports back $$6.403E0e^{8.961E-1i}$$, so the magnitude is 6.403 and the angle is 8.961E-1=0.8961 radians
 +
* Find the angle in degrees using the <code>angle()</code> command and converting the results from radians to degrees
 +
** MATH-CMPLX-angle(4), 2ND-ANS, ), ÷, D
 +
*** looks like <code>angle(Ans)/D</code>
 +
*** reports back 5.134E1, which is to say 51.34$$^{\circ}$$.
 +
Note: a previous version of this page recommended storing 1/D in R; the problem is, there will often be times that you will be using resistor values multiple times and it makes the most sense to also store those in R, which would mean overwriting this constant.  It is probably safest to just use D to go from degrees and 1/D to go from radians.
  
−
== TI 84-Plus (2024 Edition) ==
+
=== Handy Functions ===
−
The following guide was written while using a TI-84 Plus C Silver Edition.  There are subtle differences between this edition and other (TI-84 Plus CE, for example).  Anywhere "84+" shows up below refers specifically to the TI-84 Plus C Silver Edition.  As exceptions are noted, they will be posted.
+
==== Converting Representations ====
 +
If you need to convert a complex number representation between rectangular and polar (and, really, Euler), make sure the value is the most recent answer and then:
 +
* MATH-CMPLX->Rect(6) to convert an answer into rectangular (a+bi) mode
 +
* MATH-CMPLX->Polar(7) to convert an answer into polar/Euler (re^(θi)) mode
  
−
=== Complex Mode ===
 
−
By default, the calculator is not set to handle complex numbers.  If you take a factory reset 84+ and try to find the square root of -1, you will get an <code>ERROR: NONREAL ANSWERS</code>.  To set the computer up for complex numbers:
 
−
* Hit MODE to get the mode menu
 
−
* Arrow down to <code>REAL  a+bi  re^(θi)</code> and select either <code>a+bi</code> or <code>re^(θi)</code> depending on what you want the default to be
 
−
* Click ENTER and then 2ND MODE to QUIT
 
−
Now try to take the square root of -1 again.  Depending on the mode you selected, you should either get <code>i</code> or $$1e^{1.570796327i}$$
 
−
=== Converting Representations ===
 
−
If you need to convert a complex number representation between rectangular and polar:
 
−
* Hit MATH, then arrow over to the CMPLX menu
 
−
* Hit 6 if you want to go into rectangular and 7 if you want to go into polar
 
−
* Hit ENTER
 
  
−
=== Entering Values ===
+
==== Entering Values ====
−
==== Rectangular ====  
+
===== Rectangular =====  
−
* The "2ND ." key combination will produce $$i$$. 
+
* The 2ND and . key combination will produce $$i$$; it is represented as 2ND-i in the text
 
* The 84+ understands $$5i$$, $$i5$$, $$5*i$$, and $$i*5$$ to all be the same thing
 
* The 84+ understands $$5i$$, $$i5$$, $$5*i$$, and $$i*5$$ to all be the same thing
 
* If you have an initial negative sign, you need to use the unary (-) versus the binary -
 
* If you have an initial negative sign, you need to use the unary (-) versus the binary -
−
** For example, if you want just -5i, you need to enter "(-) 5 i"; starting with the regular - will generally tell the calculator to assume that you are subtracting something from the previous answer (Ans).
+
** For example, if you want just -5i, you need to enter "(-) 5 2ND-i"; starting with the regular - will generally tell the calculator to assume that you are subtracting something from the previous answer and the calculator will put '''Ans''' on the screen.
−
==== Polar ====
+
===== Polar =====
 
[[File:TI84 raddeg.PNG|thumb|TI-84 Plus C SE showing potential issue using radian-based exponentials in degree mode]]
 
[[File:TI84 raddeg.PNG|thumb|TI-84 Plus C SE showing potential issue using radian-based exponentials in degree mode]]
−
Unfortunately, the 84+ does not have an angle button for complex numbers.  It does however allow for complex exponentials. Note, however, that the exponent must be in radians, regardless of the mode of the calculator! Also, some versions of the 84+ will not allow complex exponentials while in degree mode. For those that do, you have to be exceedingly careful re-using results.
+
Unfortunately, the 84+ does not have an angle button for complex numbers.  It does however allow for complex exponentials. Note, however, that the exponent must be in radians, regardless of the mode of the calculator! Also, some versions of the 84+ will not allow complex exponentials while in degree mode. For those that do, you have to be exceedingly careful re-using results.  Best bet is to stay in (and remember that you are in) radians and convert to degrees as needed.
  
−
As an example, the polar form of $$10∠60^{o}$$ would thus be $$e^{(π/6)}$$.   
+
As an example, the polar form of $$10∠60^{o}$$ would thus be $$10e^{(π/3)}$$.   
 
* If you are in radians model, this will work fine.   
 
* If you are in radians model, this will work fine.   
−
* If you are in degree mode,  
+
* If you are in degree mode (and after everything that has been said above, why would you be???),  
 
** Some 84+ will give a domain error
 
** Some 84+ will give a domain error
 
** Others will return a value.  For those that return a value,
 
** Others will return a value.  For those that return a value,
 
*** If you are in rectangular mode, you can reuse the answer using Ans or scroll to the answer to copy and reuse it
 
*** If you are in rectangular mode, you can reuse the answer using Ans or scroll to the answer to copy and reuse it
−
*** If you are in polar mode mode, you can ruse the answer using Ans but scrolling up to copy and reuse will cause a problem since the displayed angle (in degrees) will be interpreted as radians.  See the figure at right for an example.
+
*** If you are in polar mode, you can reuse the answer using Ans but scrolling up to copy and reuse will cause a problem since the displayed angle (in degrees) will be interpreted as radians.  See the figure at right for an example.  
  
−
== CLASSWIZ ==
+
If you have an angle that is not easily converted to radians, you will need to convert degrees to radians by multiplying by $$\pi/180$$; similarly, if you find an angle in radians and want to know degrees, you will need to multiply by $$180/\pi$$. As noted above, if you have stored D as the conversion factor from degrees to radians, if you want to calculate $$10∠60^{o}$$ you can type
−
=== Complex mode ===
+
* 10, 2ND-$$e^x$$, 2ND-i, 60, ALPHA-D
−
For the CLASSWIZ to work with complex values, it needs to be in complex mode:
+
** Displays as $$10e^{i60D}$$
−
* Turn the calculator on
+
* 10, *, 2ND-$$e^x$$, 2ND-i, *, 60, *, ALPHA-D
−
* Hit the Menu button
+
** Displays as $$10*e^{i*60*D}$$
−
* Hit 2 for complex
+
In either case, the calculator should return $$1.000E1e^{1.047E0i}$$
−
To test this, try calculating the square root of negative 1.  If you get a math error, you are in the wrong mode.
 
−
=== Other settings ===
 
−
* For input and output representations - you will most likely want to set the calculator to Math Input and Decimal Output.  See p. 5 of the user's guide.
 
−
** Hit Shift and then Menu/Setup
 
−
** Hit 1 for Input/Output
 
−
** Hit 2 for MathI / Decimal0
 
−
: This will automatically convert items to floating point rather than leaving raw square roots, $$\pi$$, and the like.  If you want to convert back and forth quickly, use the $$S\leftrightarrow D$$ button.
 
−
* For angles:
 
−
** Hit shift and then Menu/Setup
 
−
** Hit 2 for Angle Unit
 
−
** Pick the unit you will generally be using - most likely degrees- all input and output will use these units for angles.
 
−
*** If you want to specify a different input unit during a calculation, enter the number then Option-Up-2 and choose the unit.  If your calculator is in radian mode, for instance $$1\angle 45$$ will give you the result for 1 at 45 radians while $$a\angle 45^o$$ will give you the results for 45 degrees(even in radians mode).
 
−
* To display values in a particular way:
 
−
** Hit Shift and then Menu/Setup
 
−
** Hit 3 for Number Format
 
−
** Sci (2) and then 5 tends to be a pretty useful way to go.
 
−
* To set the complex number display to the way you like it:
 
−
** Hit Shift and then Menu/Setup
 
−
** Scroll down one page and then type 2 for Complex
 
−
** Choose either rectangular or polar coordinates
 
  
 +
==== Displaying Angle in Degrees ====
 +
Since there are some 84+ that must be in radians to work, you may sometimes need to figure out the angle in degrees.  If you have stored variable D as noted above to be $$\pi/180$$, you can use that to efficiently get the angle in degrees.  Once you have performed the calculation:
 +
* MATH-CMPLX-angle(4), 2ND-ANS, ), /, ALPHA-D, ENTER
 +
and you will get 6.000E1 or 60 degrees.
  
−
=== Entering Values ===
+
=== Storing Values ===
−
==== Cartesian ====
+
If you are asked to perform complex calculations, you may want to store element values so that you can simply type a letter versus entering a number every time you use those values.  For example, if a problem asks you to calculate the value of:
−
Enter the real part, followed by the sign of the imaginary part, followed by $$i$$ or $$x~i$$.  Note that if the real part is negative, or if the real part is 0 and the imaginary part is negative, you need to use the unary (-) versus the binary -.
+
<center><math>
−
==== Polar ====
+
\begin{align}
−
Enter the magnitude, followed by the angle symbol (SHIFT ENG), followed by the angle in the appropriate units for how your calculator is set.  Note that the magnitude must be non-negative!  If you have a negative magnitude for a number by itself (for instance, $$-2\angle 30^o$$, you either need to enter it as 0- that number ($$0-2\angle 30^o$$) or you need to change the angle by $$\pm180^o$$ ($$2\angle -150$$)
+
\Bbb{H}(j\omega)=\frac{j\omega L}{j\omega L + R}\\
 +
L=1\mbox{mH}, R=5\mbox{k}\Omega
 +
\end{align}
 +
</math></center>
 +
for a few different values of <math>\omega</math> (say, $$10$$ rad/s and $$10^6$$ rad/s), you could do the following on your calculator:
  
−
=== Displaying Values ===
+
* Store $$1x10^{-3}$$ in L and $$5x10^{3}$$ in R: <source lang=text>
−
* To show your previous answer in polar notation:
+
1, 2ND-EE, (-), 3, STO>, ALPHA-L
−
** OPTN
+
5, 2ND-EE, 3, STO>, ALPHA-R
−
** Down
+
</source>
−
** 1
+
* Store 10 in W: <source lang=text>
−
** =
+
10, STO>, ALPHA-W
−
* To show your previous answer in rectangular notation:
+
</source>
−
** OPTN
+
* Calculate $$\Bbb{H}$$ with these values:<source lang=text>
−
** Down
+
( 2ND-i ALPHA-W ALPHA-L ) / ( 2ND-i ALPHA-W ALPHA-L + ALPHA-R )
−
** 2
+
</source>
−
** =
+
* Once you get the result, if you want to calculate the value for a different frequency, simply type<source lang=text>
−
 
+
1, 2ND-EE, 6, STO>, ALPHA-W
−
=== Complications ===
+
</source>then use the arrow buttons to go back up to where you performed the previous symbolic calculation, ENTER it to duplicate it, then ENTER it again to calculate.
−
* The CLASSWIZ will not accept complex numbers in polar form with negative magnitudes.  You can '''subtract''' a number from another, but you can not have the unary negative in front of a magnitude.
 
−
* The CLASSWIZ will not do roots of complex numbers.
 
  
 +
== TI-89 ==
 +
The following information is for the TI-89 series.  There are two major differences between the TI-89 and the 84+:
 +
* The TI-89 has a < button for entering complex numbers using polar notation.
 +
* The TI-89 will allow angles to be entered in degree mode using polar notation and will report angles in degrees using degree mode.
  
−
== TI 83+, 84+, 89 ==
+
=== Setup ===
 
* To use complex numbers on a TI-89, you need to set the right mode.  Hit the MODE button and set the following:
 
* To use complex numbers on a TI-89, you need to set the right mode.  Hit the MODE button and set the following:
 
** Angle: 2: Degree
 
** Angle: 2: Degree
 
** Complex Format: 3: Polar
 
** Complex Format: 3: Polar
−
* The 83, 84, and 89 all have the <math>i</math>.  For 83/84 it is "<2ND> ." (that is, the 2nd function button at top left followed by the decimal point in the bottom row) and for the 89 it is "<2ND> <CATALOG>"; entering a complex number in Cartesian form is thus as simple as multiplying the imaginary part by <math>i</math>.
+
* The i on a TI-89 is 2ND-CATALOG
  
−
=== Euler ===
+
=== Entering Values ===
−
* The 83, 84, and 89 all allow for complex exponentials.  Note, however, that the exponent '''must''' be in radians, regardless of the mode of the calculator!  The Euler form of <math>10\angle 60^o</math> would thus be <math>e^{(\pi/6)}</math>.
+
==== Euler ====
−
** For the 83, if you are in degree mode, the ''results'' will be in degree mode but the inputs must always be in radians.  For instance,
+
* The TI-89 allows for complex exponentials.  Note, however, that the exponent '''must''' be in radians, regardless of the mode of the calculator!  The Euler form of <math>10\angle 60^o</math> would thus be <math>e^{(\pi/6)}</math>.
−
e^(i*90)
 
−
returns
 
−
1e^(116.62i)
 
−
if the calculator is in degree mode since 90 radians simplifies to 116.62 degrees. It returns
 
−
1e^(2.035i)
 
−
if the calculator is in radian mode since 90 radians is the same as 90-28<math>\pi</math> is 2.035 radians.
 
−
** For the 84, the results are the same as for the 83 '''however''' you must be '''very careful''' if you try to use the result from a complex calculation that is reported in degree mode.  On an 84, if you enter
 
−
e^(i*90)
 
−
the result, in degree mode, is
 
−
1e^(116.62i)
 
−
If you try to up-arrow to that result and hit <ENTER> to copy it, then use it, the 84 will think of the 116.62 as a value in '''radians''' - which is to say, not at all what you meant!  If you are in degree mode, you need to refrain from using the Euler representation on an 84 or at least understand that intermediate results in Euler mode and degree mode together cannot be used later.
 
−
** For the 84, the calculator will not let you use Euler representation if you are in degree mode - you will get a domain error.  To use Euler representations on an 84, you will have to be in radian mode.
 
  
−
=== Polar ===
+
==== Polar ====
−
* Neither the 83 nor the 84 use polar representation.  You have to use Euler if you have a magnitude and an angle, and the angle must be entered in radians.
+
* The 89 has an angle button; to enter a complex number in polar notation, surround it with parentheses and separate the magnitude from the angle with the angle button, obtained with 2ND-EE.  Note that the number you put in for an angle is based on the mode the calculator is in, so if you are in degree mode,
−
* The 89 has an angle button; to enter a complex number in polar notation, surround it with parentheses and separate the magnitude from the angle with the angle button, obtained with <2ND> <EE>.  Note that the number you put in for an angle is based on the mode the calculator is in, so if you are in degree mode,
 
 
  (1<60)
 
  (1<60)
 
will be the same as
 
will be the same as
Line 125: Line 133:
 
** 2nd -(ANS) 2nd 5(MATH) 4(Complex) up(to Vector Ops) right(into menu) 5(->Rect) Enter, or
 
** 2nd -(ANS) 2nd 5(MATH) 4(Complex) up(to Vector Ops) right(into menu) 5(->Rect) Enter, or
 
** 2nd -(ANS) 2nd MODE(->) ALPHA ALPHA 2(R) /(E) )(C) T ENTER ALPHA
 
** 2nd -(ANS) 2nd MODE(->) ALPHA ALPHA 2(R) /(E) )(C) T ENTER ALPHA
−
 
−
== Storing Values ==
 
−
If you are asked to perform complex calculations, you may want to store element values so that you can simply type a letter versus entering a number every time you use those values.  For example, if a problem asks you to calculate the value of:
 
−
<center><math>
 
−
\begin{align}
 
−
\Bbb{H}(j\omega)=\frac{j\omega L}{j\omega L + R}\\
 
−
L=1\mbox{mH}, R=5\mbox{k}\Omega
 
−
\end{align}
 
−
</math></center>
 
−
for a few different values of <math>\omega</math> (say, $$10$$ rad/s and $$10^6$$ rad/s), you could do the following on your calculator:
 
−
=== CLASSWIZ ===
 
−
The CLASSWIZ only has the letters A, B, C, D, E, F, x, y, and M to store, so you have to choose where to store things.  For this example, we will store the inductor value in A and the resistor value in B.  Also note that once you hit the STO key, you will not need to hit the ALPHA button to indicate the letter.  In the keystrokes below then, the A really means hitting the (-) key and the B means hitting the...one next to it...
 
−
<source lang=text>
 
−
1 <x10x> (-) 3 <STO> A
 
−
5 <x10x> 3 <STO> B
 
−
</source>
 
−
We will store the frequency component in x:
 
−
<source lang=text>
 
−
10 * i <STO> x
 
−
</source>
 
−
to store the values.  Then, to calculate the first value,
 
−
<source lang=text>
 
−
( <ALPHA> x * <ALPHA> A ) / ( <ALPHA> x * <ALPHA> A + <ALPHA> B )
 
−
</source>
 
−
and you should get $$2.0000x10^{-6}\angle 9.0000x10^1$$
 
−
Once you get the result, if you want to calculate the value for a different frequency (say, $$10^6$$), simply type
 
−
<source lang=text>
 
−
1 <x10x> 6 * <2ND> i <STO> x
 
−
</source>
 
−
then use the arrow buttons to go back up to where you performed the previous symbolic calculation, and hit the = key to recalculate.  You will now get $$1.9612x10^{-1}\angle 8.8690x10^1$$.
 
−
 
−
 
−
=== TI ===
 
−
<source lang=text>
 
−
1e-3 <STO>> <ALPHA> l
 
−
5e3 <STO>> <ALPHA> r
 
−
</source>
 
−
To store the frequency component, on TI 83/84 plus, you will need to use ALPHA z, while on the TI 89 you can just use the z button:
 
−
<source lang=text>
 
−
10 * 2ND i STO> (ALPHA) z
 
−
</source>
 
−
to store the values.  Then, to calculate the first value,
 
−
<source lang=text>
 
−
( <ALPHA> z * <ALPHA> l ) / ( <ALPHA> z * <ALPHA> l + <ALPHA> r )
 
−
</source>
 
−
Once you get the result, if you want to calculate the value for a different frequency, simply type
 
−
<source lang=text>
 
−
1e6 * <2ND> i <STO>> <ALPHA> z
 
−
</source>
 
−
then use the arrow buttons to go back up to where you performed the previous symbolic calculation, ENTER it to duplicate it, then ENTER it again to calculate.
 
−
 
−
== Constant of Angle Conversion ==
 
−
If you are doing several complex calculations on an 83/84 and the angles you are given are in degrees, you may want to store a constant for the conversion to radians so you do not have to type in "* pi / 180" every time.  You could just put in
 
−
pi / 180 <STO>> X
 
−
and then when you need to write a complex number in Euler form, you could multiply the angle in degrees by X; for instance, to get 6<30 degrees, you could write
 
−
6*e^(i*30*X)
 
−
You can choose any letter, obviously, but X is easy to get from the <math>X,T,\Theta,n</math> button on the 83/84.
 
−
 
−
= Statics Functions =
 
−
== TI-83/84 ==
 
−
Not as many built-in functions for vectors / matrices.  See [http://www.tc3.edu/instruct/sbrown/ti83/vecprod.htm http://www.tc3.edu/instruct/sbrown/ti83/vecprod.htm] for a program that will help with cross products.
 
−
 
−
== TI-89 ==
 
−
=== Vectors in General ===
 
−
Vectors may be entered surrounded by [ ].  That is, for some vector <math>\vec{r}</math>:
 
−
<center><math>
 
−
\begin{align}
 
−
\vec{r}&=r_x\hat{\imath}+r_y\hat{\jmath}+r_z\hat{k}
 
−
\end{align}
 
−
</math></center>
 
−
say,
 
−
<center><math>
 
−
\begin{align}
 
−
\vec{r}&=3\hat{\imath}-2\hat{\jmath}+6\hat{k}
 
−
\end{align}
 
−
</math></center>
 
−
the TI version of the vector would be:
 
−
[3, -2, 6]
 
−
Note that the result will actually be surrounded by two sets of square brackets, representing a matrix.
 
−
Be sure to use the unary negative operator (-) versus the binary subtraction operator - at the start of negative entries.
 
−
=== Dot and Cross Products ===
 
−
* Vector operations on TI Calculators: [http://www.phys.lsu.edu/classes/spring2010/phys1100/TI_calc_vec.pdf www.phys.lsu.edu/classes/spring2010/phys1100/TI_calc_vec.pdf]
 
−
=== Unit Directions ===
 
−
*To find the unit direction for a vector, use
 
−
**<2nd>--<5>MATH--<4>Matrix--L:Vector ops--<1>unitV()
 
−
=== Coordinate Angles ===
 
−
*To find the coordinate angles of a vector, you should first get the unit direction vector.  Then, you must turn the unit direction vector into a list before taking the arccos of the list.  Lists are surrounded by {} instead of [].  To convert a vector to a list, use
 
−
**<2nd>--<5>MATH--<3>List--F:mat->list()<br>and put the desired matrix in as the argument; the result will be surrounded by {}.  You can then apply the arccos to the list and get all three coordinate direction angles at once!
 
  
 
= Questions =
 
= Questions =

Latest revision as of 21:41, 15 March 2024

  • 3/7 Update: This page is now almost solely focused on the TI 84+ series of calculators (with a bit of a coda on TI-89). For information on the old Casio fx-991EX series, see Calculator Tips/Classwiz.

TI 84-Plus (2024 Edition)

The following guide was written while using a TI-84 Plus C Silver Edition. There are subtle differences between this edition and other (TI-84 Plus CE, for example). Anywhere "84+" shows up below refers specifically to the TI-84 Plus C Silver Edition. As exceptions are noted, they will be posted.

Using this guide

When you are given keystrokes:

  • 2ND-Something means hit the 2ND key and then a key that has a secondary command of Something. For instance, 2ND-QUIT would mean hitting 2ND and then the key primarily labeled MODE, which has QUIT above it in the same color as the 2ND key
  • ALPHA-Letter means hit the ALPHA key and then a key that has a letter of Letter. For instance, ALPHA-D would mean hitting ALPHA and then the key primarily labeled $$x^{-1}$$, which has D above it in the same color as the ALPHA key
  • MATH-CMPLX-Command(Number) means hit the MATH button to get to the MATH menu, then use the left/right arrow buttons to scroll over to the CMPLX submenu, then use the up/down arrow buttons to scroll down to the Command command. Alternately, hit the MATH button to get to the MATH menu, then use the arrow buttons to scroll over to the CMPLX submenu, then type the Number related to the command you want. For instance, MTH-CMPLX-angle(4) will get the calculator to type angle(
  • A / means use the ÷ key (÷ is annoying to type in Mediawiki)
  • A * means use the $$\times$$ key (same reason)

Initial Setup

Modes

Modes for doing complex calculations

The default modes for the 84+ are not all useful for doing complex calculations. For instance, if you try to take the square root of a negative number with a factory-reset 84+, you will get an error! As a result, we recommend that you click the MODE button and then set the following modes before doing work:

  • SCI (for scientific notation)
  • FLOAT: 3 (to get three figures after the decimal; this yields four significant figures in scientific mode)
  • RADIAN (default; for some 84+, this must be in radians to work with complex exponentials)
  • re^(θi) to report using Euler notation - this will generally be the most useful as you will get a magnitude and a phase out of it

Click 2ND-QUIT to get out of this menu

Helpful Constants

Saving and using a constant to convert from degrees to radians

There will be times that you want to quickly convert a number from degrees to radians and vice versa. Given the number of times you may need to use these conversion factors, it may be helpful to store one of them in the calculator. Here is one recommendation:

  • Use letter D as the conversation from degrees to radians
  • Calculate $$\pi$$/180, then store it as D:
    • 2ND-PI, ÷, 180, STO>, ALPHA-D, ENTER
  • Use 1/D to convert from radians to degrees

Now if you want to calculate $$10∠60^{\circ}$$ you can type $$10e^{i60D}$$ or $$10*e^{i*60*D}$$.

Extracting an angle and using a constant to convert from radians to degrees

If you need to get an angle in degrees from a complex number, you can use the angle() command in the MATH-CMPLX menu and then divide the result by D. For instance, to determine the angle in degrees of $$4+j5$$:

  • Find $$4+j5$$ using the 84+
    • 4, +, 2ND-i, 5, ENTER
      • Looks like 4+i5
      • reports back $$6.403E0e^{8.961E-1i}$$, so the magnitude is 6.403 and the angle is 8.961E-1=0.8961 radians
  • Find the angle in degrees using the angle() command and converting the results from radians to degrees
    • MATH-CMPLX-angle(4), 2ND-ANS, ), ÷, D
      • looks like angle(Ans)/D
      • reports back 5.134E1, which is to say 51.34$$^{\circ}$$.

Note: a previous version of this page recommended storing 1/D in R; the problem is, there will often be times that you will be using resistor values multiple times and it makes the most sense to also store those in R, which would mean overwriting this constant. It is probably safest to just use D to go from degrees and 1/D to go from radians.

Handy Functions

Converting Representations

If you need to convert a complex number representation between rectangular and polar (and, really, Euler), make sure the value is the most recent answer and then:

  • MATH-CMPLX->Rect(6) to convert an answer into rectangular (a+bi) mode
  • MATH-CMPLX->Polar(7) to convert an answer into polar/Euler (re^(θi)) mode


Entering Values

Rectangular
  • The 2ND and . key combination will produce $$i$$; it is represented as 2ND-i in the text
  • The 84+ understands $$5i$$, $$i5$$, $$5*i$$, and $$i*5$$ to all be the same thing
  • If you have an initial negative sign, you need to use the unary (-) versus the binary -
    • For example, if you want just -5i, you need to enter "(-) 5 2ND-i"; starting with the regular - will generally tell the calculator to assume that you are subtracting something from the previous answer and the calculator will put Ans on the screen.
Polar
TI-84 Plus C SE showing potential issue using radian-based exponentials in degree mode

Unfortunately, the 84+ does not have an angle button for complex numbers. It does however allow for complex exponentials. Note, however, that the exponent must be in radians, regardless of the mode of the calculator! Also, some versions of the 84+ will not allow complex exponentials while in degree mode. For those that do, you have to be exceedingly careful re-using results. Best bet is to stay in (and remember that you are in) radians and convert to degrees as needed.

As an example, the polar form of $$10∠60^{o}$$ would thus be $$10e^{(π/3)}$$.

  • If you are in radians model, this will work fine.
  • If you are in degree mode (and after everything that has been said above, why would you be???),
    • Some 84+ will give a domain error
    • Others will return a value. For those that return a value,
      • If you are in rectangular mode, you can reuse the answer using Ans or scroll to the answer to copy and reuse it
      • If you are in polar mode, you can reuse the answer using Ans but scrolling up to copy and reuse will cause a problem since the displayed angle (in degrees) will be interpreted as radians. See the figure at right for an example.

If you have an angle that is not easily converted to radians, you will need to convert degrees to radians by multiplying by $$\pi/180$$; similarly, if you find an angle in radians and want to know degrees, you will need to multiply by $$180/\pi$$. As noted above, if you have stored D as the conversion factor from degrees to radians, if you want to calculate $$10∠60^{o}$$ you can type

  • 10, 2ND-$$e^x$$, 2ND-i, 60, ALPHA-D
    • Displays as $$10e^{i60D}$$
  • 10, *, 2ND-$$e^x$$, 2ND-i, *, 60, *, ALPHA-D
    • Displays as $$10*e^{i*60*D}$$

In either case, the calculator should return $$1.000E1e^{1.047E0i}$$

Displaying Angle in Degrees

Since there are some 84+ that must be in radians to work, you may sometimes need to figure out the angle in degrees. If you have stored variable D as noted above to be $$\pi/180$$, you can use that to efficiently get the angle in degrees. Once you have performed the calculation:

  • MATH-CMPLX-angle(4), 2ND-ANS, ), /, ALPHA-D, ENTER

and you will get 6.000E1 or 60 degrees.

Storing Values

If you are asked to perform complex calculations, you may want to store element values so that you can simply type a letter versus entering a number every time you use those values. For example, if a problem asks you to calculate the value of:

\( \begin{align} \Bbb{H}(j\omega)=\frac{j\omega L}{j\omega L + R}\\ L=1\mbox{mH}, R=5\mbox{k}\Omega \end{align} \)

for a few different values of \(\omega\) (say, $$10$$ rad/s and $$10^6$$ rad/s), you could do the following on your calculator:

  • Store $$1x10^{-3}$$ in L and $$5x10^{3}$$ in R: 
    1, 2ND-EE, (-), 3, STO>, ALPHA-L
5, 2ND-EE, 3, STO>, ALPHA-R
  • Store 10 in W: 
    10, STO>, ALPHA-W
  • Calculate $$\Bbb{H}$$ with these values:
    ( 2ND-i ALPHA-W ALPHA-L ) / ( 2ND-i ALPHA-W ALPHA-L + ALPHA-R )
  • Once you get the result, if you want to calculate the value for a different frequency, simply type
    1, 2ND-EE, 6, STO>, ALPHA-W
    then use the arrow buttons to go back up to where you performed the previous symbolic calculation, ENTER it to duplicate it, then ENTER it again to calculate.

TI-89

The following information is for the TI-89 series. There are two major differences between the TI-89 and the 84+:

  • The TI-89 has a < button for entering complex numbers using polar notation.
  • The TI-89 will allow angles to be entered in degree mode using polar notation and will report angles in degrees using degree mode.

Setup

  • To use complex numbers on a TI-89, you need to set the right mode. Hit the MODE button and set the following:
    • Angle: 2: Degree
    • Complex Format: 3: Polar
  • The i on a TI-89 is 2ND-CATALOG

Entering Values

Euler

  • The TI-89 allows for complex exponentials. Note, however, that the exponent must be in radians, regardless of the mode of the calculator! The Euler form of \(10\angle 60^o\) would thus be \(e^{(\pi/6)}\).

Polar

  • The 89 has an angle button; to enter a complex number in polar notation, surround it with parentheses and separate the magnitude from the angle with the angle button, obtained with 2ND-EE. Note that the number you put in for an angle is based on the mode the calculator is in, so if you are in degree mode,
(1<60)

will be the same as 

0.5+0.8660i

Displaying Values

For the TI-89:

  • To show your previous answer in polar notation:
    • 2nd -(ANS) 2nd 5(MATH) 4(Complex) up(to Vector Ops) right(into menu) 4(->Polar) Enter, or
    • 2nd -(ANS) 2nd MODE(->) ALPHA ALPHA STO(P) -(O) 4(L) =(A) 2(R) ENTER ALPHA
  • To show your previous answer in rectangular notation:
    • 2nd -(ANS) 2nd 5(MATH) 4(Complex) up(to Vector Ops) right(into menu) 5(->Rect) Enter, or
    • 2nd -(ANS) 2nd MODE(->) ALPHA ALPHA 2(R) /(E) )(C) T ENTER ALPHA

Questions

Post your questions by editing the discussion page of this article. Edit the page, then scroll to the bottom and add a question by putting in the characters *{{Q}}, followed by your question and finally your signature (with four tildes, i.e. ~~~~). Using the {{Q}} will automatically put the page in the category of pages with questions - other editors hoping to help out can then go to that category page to see where the questions are. See the page for Template:Q for details and examples.

External Links

References

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