SWBAT convert from polar coordinates to rectangular or vice versa.

Instead of left and right directions, angle measures and radii can also specify a location.

5 minutes

When we looked at rotated conic sections in an earlier lesson, my students realized that the point (1,1) could also be thought of as a rotation of 45 degrees and a distance of sqrt(2) from the origin. I remind students of this on this worksheet and use this as an** introduction to polar coordinates**. I outline my teaching strategies in the video below.

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20 minutes

Once students understand the premise behind polar coordinates, I will have them complete the table on the worksheet and** brainstorm generalizations about the conversions** from polar coordinates to rectangular and vice versa.

I encourage students to **sketch out graphs for each one and to make right triangles**. That will establish the strong connection to trigonometry. As students are working I will circulate and see how they are doing. Here is a list of things I will look for:

- Are students using Pythagorean Theorem to find the
*r*value? - If students are using inverse tangent to find the angle measure, is it in the right quadrant?
- Are students making an overgeneralization that inverse tangent will always give the correct angle when it really only works in quadrants I and IV?
- Are students sketching the locations of the points correctly?

20 minutes

Once students have had time to brainstorm, I will have students share their thoughts about these conversions with the class. I find that they usually have an easier time** converting from polar to rectangular**, than from rectangular to polar. Here are the conversions we are looking for:

It is **important that students realize** that the tan(θ) = *y/x* conversion is not perfect; they will have to think about the quadrant that the point is in and adjust the point accordingly.

The remainder of the worksheet provides an opportunity for students to graph a few points on the polar axis and to predict what some simple polar equations will look like. I encourage students to list points that satisfy each equation if they do not know what it will look like. That is usually** a helpful strategy for them to envision the graph**. We will share out our thoughts after they have a chance to think about it.

Finally, I will assign some problems from our textbook with polar coordinates. I will stick to problems that** focus on single points or very simple graphs**. We will work on more complicated equations as we progress in this unit.