Reflection: Connection to Prior Knowledge Polar Equations of Conics - Day 1 of 2 - Section 3: Extend


Students are always a little hesitant to learn the polar form of conics but by the end of the lesson they are pleasantly surprised that the process for graphing is actually easier than in rectangular form! Also the equations are simpler. When graphing, after deciding on the type of conic we usually just plug in 0, 90, 180, and 360 degrees into the equation to get a quick sketch.

At this point we have graphed limaçons, roses, and conic sections in polar form. During today's lesson it came up that these equations are all very simple in polar form but very complex in rectangular form. I asked the class why they thought that was and one student made a great observation. He said that all of these graphs have an element of "roundness" to them and since polar coordinates measures the distance from the origin and the angle, they lend themselves well to this new system. I thought it was a great point and really encapsulated the difference between polar and rectangular graphs.

  Easier than Rectangular Form!
  Connection to Prior Knowledge: Easier than Rectangular Form!
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Polar Equations of Conics - Day 1 of 2

Unit 11: Parametric Equations and Polar Coordinates
Lesson 8 of 12

Objective: SWBAT graph conic sections that are in polar form.

Big Idea: All conic sections have a directrix? Where have these been?

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Math, polar equations, Precalculus and Calculus, parabola, conic sections, hyperbola, ellipse, PreCalculus, polar coordinates
  45 minutes
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