I told her I would do all the prep work, but of course, since she’s awesome, we still spend a lot of time hashing out ideas (she’s also the Calculus teacher so she knows what to focus on and she has a ton of ways to make ideas easier–the notetakermaker was just a prettified version of her notes). As I may have previously mentioned, is the world’s best math department chair who took on a fourth prep of PreAP Precal so I didn’t have 32+ students in 3 of my classes. Now I’m sure you’re wondering how this lesson was bagel award-winning. Tomorrow we’ll practice graphing by hand and solving systems. It took most of the period to discuss and they had a matching worksheet for homework. I made this modest notetakermaker for the day: It also made the next day so much easier because they knew (a) what the graphs should look like (instead of my horrible attempts at drawing) and (b) what some parts of the equation did.
DESMOS GRAPHING POLAR COORDINATES PLUS
Plus a few of them even had time at the end and chose to spend it playing with Desmos. And they loved this! (or at least they told me they did and they were engaged and I didn’t hear any of the normal “I can’t learn unless you teach me.”) AND they made a lot of the discoveries I wanted them to, some of them more formalized than others, but all of them on the right path. Now this class hates discovery learning with the force of a thousand suns.
About 3/4 of them got through during the 50 minute class, with the rest having to finish up the last row for homework. The students worked in pairs in the computer lab and except for mention to a few of them that you can use the sliders instead of typing in each equation (I left off “ like it says in the directions” so I wouldn’t have to put a quarter in the sarcasm jar), I didn’t say anything to guide them. Here is the word file and the desmos file. My coteacher and I decided that my first draft was asking a bit too much (like the original lesson did), then I found this great worksheet and decided to base my lesson on that, using Desmos instead of the graphing calculator because DUH. I knew I wanted to use desmos and I knew I wanted them to make generalizations. Well, at least a better lesson than what was offered (which was “graph these 5 equations at the same time on the TI 83, come up with generalizations like ‘if |a|<|b| then r can be negative which forms an inner loop’, then forget what you just generalized and use a t-table to graph these.”) Plus I’m helping to write the PreAP curriculum guide so I wanted to make sure it was a good lesson. Then our school decided to teach Calculus BC this year and–oops!–turns out that skill is kind of an important thing. While I did enjoy seeing where the petals and loops came from, we only got through 6 graphs and we didn’t really delve into recognizing the different equations and being able to do a quick sketch. Last year, we did some converting back and forth between polar and rectangular equations and then spent a day on graphing polar equations using t-tables.
Typing out "theta" automatically inserts θ, and typing out "pi" automatically inserts π. Important Notes and Useful Tips for Using the Desmos Calculator:įor powers of trigonometric functions, powers other than 2 and -1, we need to use brackets instead.įor example: cos4θ needs to be written instead as either cos(θ)4 or (cosθ)4įor parametric equations, we use the t parameter to graph the curve, but can use other English letters (so θ won't work) to graph individual points.įor polar curves, we need to r = f(θ) using other variables will be viewed as a Cartesian curve. Note: Some machines require that the parameter be called t rather than θ. In this case we take the polar equation r = f(θ) and write its parametric equations as: With other machines we need to convert to parametric equations first. Some graphing devices have commands that enable us to graph polar curves directly. Polar Coordinates: Graphing Polar Curves with Graphing DevicesĪlthough it's useful to be able to sketch simple polar curves by hand, we need to use a graphing calculator or computer when we are faced with a curve as complicated as the ones shown below: USEFUL TIP: If I'm going too fast or too slow, play this video at a different speed.
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DESMOS GRAPHING POLAR COORDINATES PDF
Download PDF Notes: !As32ynv0LoaIhvQ0qj1PLNzLNFnhIwĭownload These Notes: Link is in Video Description.
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