![]() Unfortunately, Desmos does not support complex numbers. Luckily, the parameterization of the complex unit circle is exactly the same as the parameterization of the unit circle in the real plane (excluding the imaginary unit of course). In the Desmos graph I took advantage of this fact to rotate each point. To rotate an entire curve (as opposed to a single point), I made a parametric function of $t$ and applied the transformation to each point $(t, f(t))$ in the domain $a\leq t \leq b$. I like this one because of the simplicity. I also like it because I had no idea how to do calculus when I created it about a year and a half ago. However, I did understand that the derivative magically yields the slope of the function at any given point. So I decided to create a little demonstration, and this is probably one of the first things that got me seriously interested in math. The black curve is the function (you can edit it from the link above), the red line is the tangent, and the blue line is the normal. This graph shows the functions that yield the $x$ and $y$ coordinates of a point as it moves around an ellipse. This is analogous to the $\sin$ and $\cos$ functions for a circle. In fact, if you set $a=c_0$ and $b=c_0$ in the graph above for some $c_0\neq 0$, the resulting functions will be the sine and cosine. The blue curve is an analog of cosine, and the red is an analog of sine. I don’t know of any applications for this, but it is pretty interesting to see how the shape of these functions change depending on the characteristics of the ellipse. For example, from the image above, you can tell the major axis is in the $x$ direction because the cosine analog has a greater range than the sine analog. Here are some tutorials on how to use :ĪND, my final bit of advice is to join Twitter and follow Desmos.The top and bottom of the blue curve are pinched together because the direction of the point moving along the circle is rapidly changing since the ellipse is wider than it is tall. If you’re a teacher, you really should check out Play around with anything you can in Desmos! Graphing should be (and can be) fun! Here are some great art examples Desmos has curated. ![]() Once you have a reasonable working knowledge of Desmos, practice by making a mathy graph, or try making a picture! You can see my very first (ever) attempt at a picture followed by the improved version I made with just a little more time and effort. Here are some great math examples Desmos has curated. Once you feel comfortable with the basics, branch out into any of the other topics on that look interesting to you! I recommend regressions, restrictions, and lists. Not sure where to start? How about with some of these basics: If you like reading manuals, here’s a pdf user guide, and if you like having a paper version, it’s only 13 pages long so it’s easy to print! ![]() To learn as much as you can about learn how Desmos works, the best thing you can do for yourself is get on over to to watch video tutorials and try some interactive tours. But if you’d like a more structured approach, here’s my advice! The Desmos team has worked hard to make it as user friendly as possible. Many people begin learning about Desmos without any official help, just trying it out. Hi there! If you’re new to Desmos, you’re in for a treat! It’s everything you ever wanted a graphing calculator to be.
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