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## Desmos and LaTex Mashup

Over the past year, I have  created a lot of graphs in Desmos.  A collection of these can found here.  There you will find a wide range of graphs; some  are art related and some are only using sliders.  Also, some of the graphs are lab based and explorations.  These graphs have instructions for students to follow and some blank spots for their answers.  However, I have wanted students to work on paper, too, while working in Desmos.  So, I am now creating a Desmos Lab packet.  This lab packet will look very similar to the Desmos graph, allowing students to work through Desmos and record their work on paper.  Here are the steps if you would also like to create a worksheet/lab for students to follow.

1. Go to this website. http://jsfiddle.net/uRkkM/3/ The directions are in the lower right hand corner.  All you have to do is drag “Equations List” to your bookmarks bar.  Then, “From a Desmos Graph, it will open a new window containing text and latex for the expressions from the expressions list.”
2. Now create a lab or some type of exploration in Desmos.  When done click the “Equations List” and you will see all of the inputs from you Desmos graph that can be copied in LaTex.
3. Finally, polish up your LaTex file.  Now your students have a piece of paper that they can easily follow along with the Desmos graph.

There you go simple as that!  I am excited to try this out with my students.  Here is a link to what my looks like so far. Check it out and let me know if you have any ideas.

Here are is an example of those steps.

• The Desmos graph is here: https://www.desmos.com/calculator/yw9lovl86i
• The input after pressing Equations list looks like this.  I copy it and paste it into a LaTex document
Semi Circle with radius 'a'.
$f\left(x\right)=\sqrt{a^2-x^2}$
$a=4$
Below are two points on the semi-circle, such that the line connecting the two is parallel to the x-axis and is a factor 'b' of the diameter.
$\left(ba,\space f\left(ba\right)\right),\space\left(-ba,\space f\left(-ab\right)\right)$
A factor "b" of the diameter. For example, b=0.5 means that the top blue line half of the diameter. b=0.2 would be two tenths of the diameter, or in other words, one-fifth.
$b=0.8$
Begin by letting a=2 and b=0.5.  What is the height between the two blue lines?
Next let a=4 and b=0.5. What is the height between the two blue lines?
Try more 'a' and 'b' values till you see a pattern.  See if you can write the height as function of b.
Your answer above probably has some trig functions involved.  See if you can write the equivalent algebraic expression.
$H_{eight}\left(x\right)=ax\tan\left(\arccos\left(x\right)\right)$
$y=a\sqrt{1-x^2}$
$\left(b,\space H_{eight}\left(b\right)\right)$
$y=\left\{-ab\le x\le ab:f\left(ab\right)\right\}$
$y=\left\{-a\le x\le a:0\right\}$