Reflection: Connection to Prior Knowledge Graphing Polar Equations - Section 2: Explore

 

Factoring was a common strategy to isolate r when students were converting from rectangular to polar form. Questions #3c and #3d were really interesting because they both involved factoring but many students were getting an incorrect answer for #3d but not for #3c. As shown in the image, students factored an r out of both equations and then divided.

For #3d, when I asked students was r = 0 would look like, they knew that it would be a point at the origin and not the linear graph we were looking for. To get them back on track, we had to recall what we learned when we were solving trig equations - that when dividing by a variable you can lose a solution. In this case we were losing a solution - the correct one! Since we knew that r = 0 was definitely not the correct equation, it was okay to divide both sides by r, however, since it is okay to lose r = 0.

Another was to approach this would be to set both of the factors from #3d equal to zero, and to solve both and choose the one that would be the same graph as y = 2x.

  Connection to Prior Knowledge: Factoring Challenges
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Graphing Polar Equations

Unit 11: Parametric Equations and Polar Coordinates
Lesson 5 of 12

Objective: SWBAT convert from rectangular equations to polar equations.

Big Idea: Use the polar/rectangular conversions for entire graphs.

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