Just got my TI-Nspire CAS, have a few small questions
Seventh Helix
have found this site, I've no idea how I'd use this beast to its full
potential!
Anyways, I have a few questions, mostly about the graphing section.
I've never owned a graphing calculator before, so this is all
completely new to me. I'm also a Grade 12 student (Just finished Pre-
Calculus, now working on a Calculus AP course for the rest of the
year.), I've always done well in math, but a lot of the things people
say on this website go way over my head, so I appologize if that
happens! :)
-Is there any way to graph a conic section? Things like Elipses and
Hyperbolas from their equation? I thought I'd seen a picture long ago
of an Nspire's screen that had a Hyperbola graphed, while showing its
equation, as well as the asymptopes and everything. Is this possible?
-When graphing things like rectangles, triangles, circles, etc, is
there any way to graph it to exact specifications? Is it possible to,
say, graph a right-angle triangle with the A side of 3, a B side of 4,
and for it to automatically calculate that the last side is 5, then
display the triangle, showing the lengths of each side, the perimeter,
and the area? Sure it might be a bit cluttered, but if I wanted to do
something like this, would it be possible?
-I've been able to draw a rectangle in the Plane Geometry view (Though
I'm really not sure of the difference between it and the Graphing
view...) and make it display the perimeter and area. I've been able to
lock the perimeter value, and move the points around, finding the
maximum area possible. Is it possible, after this max area has been
found, to display the length of each side? It's great to be able to
easily find the maximum area like this, but it doesn't seem
particularily useful to me to not know the lengths that give you that
maximum as well.
-Similar to the last two questions, is there a way to display the
coordinates of each point (and maybe edit them if I want to) on a
specific shape? I've seen pictures of older TI calculators displaying
a triangle that was split up into different sections, showing the
coordinates of each point as well as the length of each side. Is this
possible to do on the TI-Nspire CAS?
-Say I have a problem that revolves around a specific point on a
graph. Is it possible to specifically plot a point at (2,5) and then
work at it from there? I've been able to plot a point using the axis
and grid to help, but what if I want to plot an oddly placed point
such as (1.4,5.3)? Is there any way to do this easily?
These might be easy to answer questions, or hard ones. Like I said,
I'm really new to this whole thing, but it's definitely very exciting!
I'm looking forward to using this powerhouse in my upcoming physics,
chemistry, and calculus classes!
Thank-you so much, all. I look forward to your advice.
John Hanna
x^2 + y^2 = 25 becomes
y = +-sqrt(25-x^2)
To graph it, enter f1(x)={1,-1}sqrt(25-x^2)
The {1,-1} represents the '+-'.
So any conic can be graphed this way, even those with an xy term (you'd have
to use the Quadratic Formula for those using y as the thing to solve for).
And then there are conics constructions, too.
If you have a TI-Nspire CAS then there's a Conics file in the Examples
folder. It does plotting and solving.
John Hanna
jeh...@optonline.net
973.398.3815
T3 - Teachers Teaching with Technology
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Nelson Sousa
- John already answered the first, so I'll skip that. Just remember
that conic sections are not graphs of functions. You need two
functions to draw them (except the parabola if it's vertically
oriented);
- To create a triangle with exact specifications I'd reccommend the
following: create a point; write the side lengths you want; create
circles of desired radius by clicking on the point then on the text
box; draw a vertical line and a horizontal line (press and hold
shift), find the appropriate intersections between lines and circles.
Now you have the 3 vertices and can draw the triangle.
- Differences between graphs and geometry are subtle; in graph view
you have a axes, so you have coordinates. You can adjust the window
settings and create a non-isometric window; in geometry view there are
no coordinates, the view is always isometric (so that a circle always
looks like a circle). Measurements in graph view come in u (units)
whereas in geometry view you can edit the scale and define the units
you want (default is cm). As to determining the maximum area: when
your fixed perimeter rectangle is defined measure the area and the
length side and store them into variables; go to a spreadsheet page
and capture the coordinates' values (define two columns as
=capture(area,1) and =capture(side,1); name those two columns (xlist
and ylist) and plot them as a scatter plot. Your plot will resemble a
parabola. So, do a quadratic regression and plot the regression
function. Trace it in order to find the maximum; see the PDF document
available at http://www.nelsonsousa.pt/index.php?lang=en&cat=2&subcat=9&article=56
The document is in Portuguese but you seem to be clever enough to read
through the screen shots ;)
- Yes, just select Coordinates and Equations and click the points you
want. This is valid only in Graph view, in Geometry view there is no
concept of coordinates.
- Generally anything that can be created and displayed can be edited;
create a point and display its coordinates; now double click one of
the coordinates (with no tool selected). Enter the number you wish.
There you have it! You can do this with function definitions, axes
endpoints, tick marks, lengths of segments and vectors (as long as
they're defined creating the endpoints on the fly, if they're created
as dependent objects of pre-existing points you can't), etc.
All these methods can be done with the standard Nspire, you
don't need CAS for any of them.
Let me know if you have any trouble following these directions.
They're somewhat compact and cryptic.
Cheers,
Nelson