![]() ![]() Here’s what Desmos will graph:īut if we convert this to parametric, we can see the entire curve! Or let’s look at this polar function with a period of 17π. Now check it out with positive andnegative values of t: Here it is for only positive values of θ, or t, after the polar-to-parametric conversion : Let’s take another look at that spiral, using parametric equations instead of polar. This is fantastic if you want to graph something where the curve won’t be complete after 12π radians. Notice that it allows you to specify a domain. In Desmos, parametric equations are written as an ordered pair, kind of like a point: However, if you put them into Desmos like this, you won’t get the graph you expected at all. In order to define x and y independently of each other, we will use the polar-to-rectangular conversion as follows:ĭesmos requires parametric equations to be written in terms of the parameter t and not θ, like you see below. The idea is just that you have separate equations to define what x is doing and what y is doing. These little guys are the bread and butter of so much of the amazing stuff that can be graphed on Desmos. If you’re unfamiliar with parametric equations, this is truly your lucky day. Never fear! You CAN view a polar graph for any values of θ that you want, you just have to convert it to parametric first.įor my example of how to convert polar to parametric, I’ll use this pretty little curve. For example, what happens when θ is negative? What about for larger values of θ? This suffices for many basic graphs, but even in the case of this spiral, it means that we aren’t seeing the whole picture. As far as I can tell, it will only draw polar graphs for values of θ from 0 to 12π radians: But as of right now, you cannot specify the domain of a polar function on Desmos. And when you graph them on Desmos, they’re simply stunning. The curves polar functions generate are fun and unexpected. This post may help to explain one of the reasons behind my change of heart. What’s your favorite type of equation? I have always loved polar equations, but in the last year or so, parametric equations have taken polar’s place as #1. (hint: it involves a quick switch to parametric equations.) In today’s post: a work-around for specifying the domain of a polar functions.
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