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#### b^3

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##### Guide to Using the TI-Nspire for SPECIALIST  The intricate and tightly packed
« on: October 08, 2011, 05:20:48 pm »
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Version 2.00
Ok guys and girls, this is a guide/reference for using the Ti-nspire for Specialist Maths. It will cover the simplest of things to a few tricks. This guide has been written for Version 3.1.0.392. To update go to http://education.ti.com/calculators/downloads/US/Software/Detail?id=6767

Any additions or better methods are welcomed. Also let me know if you spot any mistakes.

Guide to Using the Ti-nspire for METHODS - The simple and the overcomplicated: http://www.atarnotes.com/forum/index.php?topic=125386.msg466347#msg466347

NOTE: There is a mistake in the printable version. Under the shortcut keys the highlighting should read "Copy: Ctrl left or right to highlight, [SHIFT (the one with CAPS on it)] + [c]"

Simple things will have green headings, complicated things and tricks will be in red. Firstly some simple things. Also Note that for some questions, to obtain full marks you will need to know how to do this by hand. DONT entirely rely on the calculator. Remember this should help speed through those Multiple Choice and to double check your answers for Extended Respons quickly.

Solve, Factor & Expand
These are the basic functions you will need to know.
Open Calculate (A)
Solve: [Menu] [3] [1]  (equation, variable)|Domain
Factor: [Menu] [3] [2]  (terms)
Expand: [Menu] [3] [3]  (terms)

Vectors
These way the Ti-nspire handles vectors is to set them up like a 1 X 3 matrix. E.g. The vector 2i+2j+1k would be represented by the matrix $\begin{bmatrix}
2 & 2 & 1
\end{bmatrix}$
You can enter a matrix by pressing [ctrl] + ["x"], then select the 3 X 3 matrix and enter in the appropriate dimensions.
Its easier to work with the vectors if you define them. E.g. [Menu] [1] [1] a = $\begin{bmatrix}
2 & 2 & 1
\end{bmatrix}$

The functions that can be applied to the vectors are:
Unit Vector: [Menu] [7] [C] [1] - unitV($\begin{bmatrix}
x & y & z
\end{bmatrix}$
)
Dot Product: [Menu] [7] [C] [3]  dotP($\begin{bmatrix}
a & b & c
\end{bmatrix}$
,$\begin{bmatrix}
x & y & z
\end{bmatrix})$

Magnitude: type "norm()"  norm($\begin{bmatrix}
a & b & c
\end{bmatrix}$
)
E.g. a=2i+2j+k, b=6i+2j-16k, Find the Unit vector of a and a.b

E.g. a and b are perpendicular

Graphing Vectors Equations
Normally expresses as a function of t. Graphed as parametric equations. Select the graph entry bar, [ctrl] + [Menu] [2:Graph Type] [2:Parametric]
Enter in the i coefficient as x1(t) and the j coefficient as x2(t)
e.g. Graph $f(t)=2e^{0.3t}\cos(2t)\mathbf{\vec{i}}+2e^{0.3t}\sin(2t)\boldsymbol{\vec{j}}$

Complex Numbers
There are two important functions related to complex numbers. They work the same as the original functions, but will give complex solutions aswell.
E.g. Solve $z^{2}+4z-4=0$ for z and factorise $z^{3}+z^{2}+z+1$

Quicker Cis(θ) Evaluations
1. Define ([Menu] [1] [1]) cis(θ)=\cos(θ)+i\sin(θ)
2. Simply plug in the value of theta

Finding Arguments
1. Use the angle function (i.e. find it in the catalogue of type angle(*)
E.g. Find the Argument of $\frac{\sqrt{2}}{2}+\frac{\sqrt{2}}{2}\boldsymbol{i}$

Defining Domains
While graphing or solving, domains can be defined by the addition of |lowerbound<x<upperbound
The less than or equal to and greater than or equal to signs can be obtained by pressing ctrl + < or >
e.g. Graph $y=x^{2}$ for $x \in (-2,1]$
Enter $f2(x)=x^2 |-2 into the graphs bar

This is particulary useful for fog and gof functions, when a domain is restriced, the resulting functions domain will also be restricted.
E.g. Find the equation of $fog(x)$ when $f(x)=x^2,x \in(-2,1]$ and $g(x)=2x+1,x\in R$
1. Define the two equations in the Calulate page. [Menu] [1] [1]

2. Open a graph page and type, f(g(x)) into the graph bar

The trace feature can be used to find out the range and domain. Trace: [Menu] [5] [1]
Here $fog(x)=(2x+1)^{2}$ where the Domain = (-1.5,1] and Range =[0,4)

Completing the Square
The easy way to find the turning point quickly. The Ti-nspire has a built in function for completing the square.
e.g. Find the turning point of $y=2x^2+8x+9$

So from that the turning point will be at (-2,1)

Easy Maximum and Minimums
In the newer version of the Ti-nspire OS, there are functions to find maximum, minimums, tangent lines and normal lines with a couple of clicks, good for multiple choice, otherwise working would need to be shown. You can do some of these visually on the graphing screen or algebraically in the calculate window.
Maximums: [Menu] [4] [7]  (terms, variable)|domain
Minimums: [Menu] [4] [8]  (terms, variable)|domain
E.g. Find the values of x for which $y=2x^{3}+x^{2}-3x$ has a maxmimum and a minimum for $x\in [-\frac{3}{2},2]$

Tangents at a point: [Menu] [4] [9]  (terms, variable, point)
Normals at a point: [Menu] [4] [A] - (terms, variable, point)
E.g. Find the equation of the tangent and the normal to the curve $y=(x+2)^{2}$ when $x=1$.

Graph f(x) and g(x), then graph f(x)+g(x)
E.g. Graph $x^{2}+\frac{1}{x}$
Then $f(x)=x^{2}, g(x)=\frac{1}{x}$

Finding Vertical Asymptotes
Vertical Asymptotes occur when the function is undefined at a given value of x, i.e. when anything is divided by 0. We can manipulate this fact to find vertical asymptotes by letting the function equal $\frac{1}{0}$ and solving for x.
e.g. Find the vertical asymptotes for $y=sec(x),x\in[-2\pi,2\pi]$

So for $y=sec(x),x\in[-2\pi,2\pi]$ there is a vertical asymptotes at $x=\frac{-3\pi}{2}, x=\frac{-\pi}{2}, x=\frac{\pi}{2}$ and $x=\frac{3\pi}{2}$
Dont forget to find those other non-vertical asymptotes too.

The x-y Function Test
Every now and then you will come across this kind of question in a multiple choice section.
If $f(x)+f(y)=f(xy)$, which of the following is true?
A. $f(x)=x^2$
B. $f(x)=\ln(x)$
C. $f(x)= \frac{1}{x}$
D. $f(x)=x$
E. $f(x)=(x+2)^2$
You could do it by hand or do it by calculator. The easiest way is to define the functions and solve the condition for x, then test whether the option is true. If true is given, it is true otherwise it is false.

So option B is correct.

The Time Saver for Derivatives
By defining, f(x) and then defining df(x)= the derivative, you wont have to continually type in the derivative keys and function. It also allows you to plug in values easily into f(x) and f(x).
E.g. Find the derivative of $y=2x^3+3x^2-4x+2+ \frac{1}{x}$
Define f(x), then define df(x)

The same thing can be done for the double derivative.

Just remember to redefine the equations or use a different letter, e.g. g(x) and dg(x)

Implicit Differentiation
[Menu] [4] [E] impDif(equation, variable 1, variable 2)
E.g. Differentiate $xy+\frac{1}{x}+\frac{1}{y}=5$ with respect to x.

Solving For Coefficients Using Definitions of Functions
Instead of typing out big long strings of equations and forgetting which one is the antiderivative and which one is the original, defined equations can be used to easily and quickly solve for the coefficients.
E.g. An equation of the form $y=ax^3+bx^2+cx+d$ cuts the x-axis at (-2,0) and (2,0). It cuts the y-axis at (0,1) and has a local maximum when $x=-1$. Find the values of a, b, c & d.
1. Define $f(x)=ax^3+bx^2+cx+d$ (Make sure you put a multiplication sign between the letters)
2. Define the derivative of the f(x) i.e. df(x)
3. Use solve function and substitute values in, solve for a, b, c & d.

So $a=\frac{-1}{2}, b=\frac{-1}{4}, c=-2$ and $d=1$ and the equation of the curve is $f(x)=\frac{1}{2}x^3-\frac{1}{4}x^2-2x+1$

Deriving Using the Right Mode
The derivative of circular functions are different for radians and degrees. Remember to convert degrees to radians and be in radian mode, as the usual derivatives that you learn e.g. $\frac{d}{dx}(\sin(x))=\cos(x)$ are in radians NOT degrees.

Getting Exact Values On the Graph Screen
Now for what you have all been dreaming of. Exact values on the graphing screen. Now the way to do this is a little bit annoying.
1. Open up a graph window
2. Plot a function e.g. $f(x)=\sqrt[3]{x}$
3. Trace the graph using [Menu] [5] [1]
4. Trace right till you hit around 0.9 or 1.2 and click the middle button to plot the point.
5. Press ESC
6. Move the mouse over the x-value and click so that it highlights, then move it slightly to the right and click again. Clear the value and enter in $\frac{1}{2}$
.

Using tCollect to simplify awkward expressions
Sometimes the calculator wont simplify something the way we want it to. tCollect simplifies expressions that involves trigonometric powers higher than 1 or lower than -1 to linear trigonometric expressions.

Differntial Equation Solver
[Menu] [4] [D]  DeSolve(equation, variable on bottom, variable on top)

Integrals
E.g. If find $y$ if $\frac{dy}{dx}=\frac{2}{\sqrt{4-x^{2}}}$ and y=0 when x=0

Plotting Differential Equations + Slope Fields
Firstly you will need to open a graphing screen.
Then you need to setup up the mode for differential equations. This can be done in two ways:
A. Select the graph entry bar and press [Ctrl] [Menu] then select [2] (Graph Type) [6] (Differential Equation)
or
Now the interface comes up.

NOTE 1: When entering y in the bar, you will have to enter y1.
NOTE 2: If you want to plot a second differential equation that is not related to the first, you will need to either, open a new document (not just a graphing screen, for some reason the original equation that you plotted will be shown again) or clear out all the differential equations in the graph entry bar (i.e. y1, y2...) or open a new problem in the current document by pressing [Ctrl] [Home] [4] [1] [2]
e.g. Sketch the slope field $\frac{dy}{dx}=\sin(x)$

e.g. Sketch the slope field of  $\frac{dy}{dx}=x+y$ for $x=-2, -1, 0, 1$
NOTE: Make sure you use y1

You will only need to draw the lines in the red box since $x=-2, -1, 0, 1$ if you draw the unrequited lines you may lose marks
e.g. Sketch the slope field for $\frac{dy}{dx}=x^{2}+x$ with initial conditions x=1 when y=0

Dont forget a slope field should have a table of values with it.

Graphing Circles, Elipses, Hyperbolas in 1.5 easy steps
This allows you to plot equations in their zero form easily without having to rearrange for y and forming two (or more) equations.
Step 0: Firstly what you have to is rearrange the equation so that it equals 0.
e.g. $x^{2}+y^{2}=4$ becomes $x^{2}+y^{2}-4=0$
$x^{2}-y^{2}=4$ becomes $x^{2}-y^{2}-4=0$
$x=(y-3)^{2}-2$ becomes $x-(y-3)^{2}+2=0$
Now remove the $=0$ part
Step 1: Enter in the graph bar zeros(equation, dependent variable)

Shortcut Keys
Copy: Ctrl left or right to highlight, [SHIFT (the one with CAPS on it)] + [c]
Paste: [Ctrl] + [v]
Insert Derivative: [CAPS] + ["-"]
Insert Integral: [CAPS] + ["+"]
∞: [Ctrl] + [i]

Thanks to Jane1234 & duquesne9995 for the shortcut keys. Thanks to vgardiy for the real easy sketching of equations in their zero form.

Remember you can always do other funs things like 3-D graphs. Enjoy. Yey 800th post.

« Last Edit: June 29, 2012, 08:44:12 pm by b^3 »
2012-2016: Aerospace Engineering/Science (Double Major in Applied Mathematics - Monash Uni)
TI-NSPIRE GUIDES:

Co-Authored AtarNotes' Maths Study Guides

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#### tony3272

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##### Re: Guide to Using the Ti-nspire for Specialist  The intricate and tightly packed
« Reply #1 on: October 08, 2011, 05:27:18 pm »
0
Great job

Also if you want to do stuff with complex numbers on you cas you can also go: $rcis(x)=re^{ix}$, as the calc doesn't have a cis function.
2010 : Accounting
2011 : Methods (CAS) | Chemistry  | Physics  | English Language  | Specialist Maths

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##### Re: Guide to Using the Ti-nspire for Specialist  The intricate and tightly packed
« Reply #2 on: October 08, 2011, 05:34:13 pm »
0
Those 3D graphs are cool

#### b^3

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##### Re: Guide to Using the Ti-nspire for Specialist  The intricate and tightly packed
« Reply #3 on: October 08, 2011, 05:37:30 pm »
+1
Great job

Also if you want to do stuff with complex numbers on you cas you can also go: $rcis(x)=re^{ix}$, as the calc doesn't have a cis function.
Yeh once you defined it to be cos(x)+isin(x) it automatically simplfies it to that untill you start pluging numbers in. I'm just trying to fix up all the links now.
2012-2016: Aerospace Engineering/Science (Double Major in Applied Mathematics - Monash Uni)
TI-NSPIRE GUIDES:

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#### b^3

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##### Re: Guide to Using the Ti-nspire for Specialist  The intricate and tightly packed
« Reply #4 on: October 08, 2011, 06:08:49 pm »
0
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TI-NSPIRE GUIDES:

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#### vea

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##### Re: Guide to Using the Ti-nspire for SPECIALIST  The intricate and tightly packed
« Reply #5 on: October 08, 2011, 06:53:00 pm »
0
Great guide! The TI seems so much better than the Casio...
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#### HCbigstick

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##### Re: Guide to Using the Ti-nspire for SPECIALIST  The intricate and tightly packed
« Reply #6 on: October 08, 2011, 07:01:14 pm »
0
This is awesome man thanks heaps!

#### SamiJ

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##### Re: Guide to Using the Ti-nspire for SPECIALIST  The intricate and tightly packed
« Reply #7 on: October 08, 2011, 07:14:01 pm »
0
2010: Biology [100]
2011: English [61]
Mathematical Methods (CAS) [75]
Chemistry [84]
Physics [99]
Psychology [∞]
2012:....

#### b^3

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##### Re: Guide to Using the Ti-nspire for SPECIALIST  The intricate and tightly packed
« Reply #8 on: October 08, 2011, 07:17:45 pm »
0
(Image removed from quote.)(Image removed from quote.)
(Image removed from quote.)(Image removed from quote.)
These are wicked! Do you need the new software to do them?
As far as I know, you need the newer version to do it with, but there are all these new functions here and three that make checking you asnwers easier and quicker, so it's a good ide to upgrade. They got rid of a lot of the bugs too. If you do upgrade, when you are on the graphing window press menu, then 2:view, then 3: 3d graphing.
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TI-NSPIRE GUIDES:

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I'm starting to get too old for this... May be on here or irc from time to time.

#### jane1234

• Guest
##### Re: Guide to Using the Ti-nspire for SPECIALIST  The intricate and tightly packed
« Reply #9 on: October 08, 2011, 07:26:41 pm »
0
Wow thanks, never knew the expand tool gave you partial fractions.

Do you know if there is any way to use the 3D graphs to somehow plot vectors with i,j & k? For example, showing what i + 2j - 3k would look like? I was trying to figure this out hmm...

#### b^3

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##### Re: Guide to Using the Ti-nspire for SPECIALIST  The intricate and tightly packed
« Reply #10 on: October 08, 2011, 07:33:28 pm »
0
Wow thanks, never knew the expand tool gave you partial fractions.
Yeh it makes life easier. And WOW I just worked out how to rotate the 3d-graphs.
Do you know if there is any way to use the 3D graphs to somehow plot vectors with i,j & k? For example, showing what i + 2j - 3k would look like? I was trying to figure this out hmm...
I don't think it can but I'll have a look around and post back if I figure anything out.
2012-2016: Aerospace Engineering/Science (Double Major in Applied Mathematics - Monash Uni)
TI-NSPIRE GUIDES:

Co-Authored AtarNotes' Maths Study Guides

I'm starting to get too old for this... May be on here or irc from time to time.

#### SamiJ

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##### Re: Guide to Using the Ti-nspire for SPECIALIST  The intricate and tightly packed
« Reply #11 on: October 08, 2011, 07:35:41 pm »
0
And WOW I just worked out how to rotate the 3d-graphs.
This is crazy!
2010: Biology [100]
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#### jane1234

• Guest
##### Re: Guide to Using the Ti-nspire for SPECIALIST  The intricate and tightly packed
« Reply #12 on: October 08, 2011, 07:36:49 pm »
+1
Wow thanks, never knew the expand tool gave you partial fractions.
Yeh it makes life easier. And WOW I just worked out how to rotate the 3d-graphs.
Do you know if there is any way to use the 3D graphs to somehow plot vectors with i,j & k? For example, showing what i + 2j - 3k would look like? I was trying to figure this out hmm...
I don't think it can but I'll have a look around and post back if I figure anything out.

Haha have you clicked auto rotation yet? It'll spin around on its own... I think this could potentially amuse some people for hours...

#### b^3

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##### Re: Guide to Using the Ti-nspire for SPECIALIST  The intricate and tightly packed
« Reply #13 on: October 08, 2011, 07:38:41 pm »
+1
Wow thanks, never knew the expand tool gave you partial fractions.
Yeh it makes life easier. And WOW I just worked out how to rotate the 3d-graphs.
Do you know if there is any way to use the 3D graphs to somehow plot vectors with i,j & k? For example, showing what i + 2j - 3k would look like? I was trying to figure this out hmm...
I don't think it can but I'll have a look around and post back if I figure anything out.

Haha have you clicked auto rotation yet? It'll spin around on its own... I think this could potentially amuse some people for hours...
I have now and woow, there goes the rest of my holidays.
2012-2016: Aerospace Engineering/Science (Double Major in Applied Mathematics - Monash Uni)
TI-NSPIRE GUIDES:

Co-Authored AtarNotes' Maths Study Guides

I'm starting to get too old for this... May be on here or irc from time to time.

#### b^3

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##### Re: Guide to Using the Ti-nspire for SPECIALIST  The intricate and tightly packed
« Reply #14 on: October 08, 2011, 07:45:32 pm »
+1
Just worked out how to find the magnitude of a vector.
Type Norm([1 3 4]) e.t.c.
I'll probably add it to the post here later, but won't be able to add it to the notes pdf doc.
2012-2016: Aerospace Engineering/Science (Double Major in Applied Mathematics - Monash Uni)
TI-NSPIRE GUIDES:

Co-Authored AtarNotes' Maths Study Guides

I'm starting to get too old for this... May be on here or irc from time to time.