![]() The variable 'n' represents the b term 2π/b determines the period (distance between repetitions of the graph). Just as when graphing on the Cartesian plane, the variable 'a' determines the size (amplitude) of the curve. Polar roses can be created using the equations r = a cos( n θ) or r = a sin( n θ). With this in mind, we can make polar roses, cardioids, and lemniscates. This opens up a world of possibilities because coterminal angles (π/2 and 5π/2, for example) will have the same value of cosine or sine, and instead of going on forever in waves, they will be bounded by those values of r and theta. #Desmos graphing sine and cosine series#The polar coordinate system looks like a series of concentric circles representing r centered at the origin. If we graph on the polar axis, we graph in terms of r and theta (the angle measure). If you plot y=sinx or y=cosx on the Cartesian (x,y) plane, you get the familiar waves that are anchored on the x-axis. When we talk about sine, cosine, and tangent functions and their reciprocals, we are talking about what are called periodic functions, meaning that they repeat values at regular intervals. So for anyone with a little precalc background, let's talk polar roses and their cousins. So I've been teaching her some topics that she hasn't yet gotten to in class (and I'm nervous that with all that's going on, she WON'T get to at all), and one of these topics has been things involving trig and polar equations of all sorts. One of my students is prepping for the SAT, and that prep includes prep for the Math SAT II. However, with all the doom and gloom we have in the news, and because while we've been self isolating in our houses, spring has arrived, I figured I'd change gears today and head back to math activities. My original plan was to publish another long form rant, this time about the murder of Thomas Becket in 1170 (I have a soft spot for everything related to Henry II of England). ![]()
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