Lesson 8.1
Plotting and Equivalent Representations
Polar coordinates give a signed distance and direction. Adding full turns preserves the point. Negating the radius reverses direction, so add pi to the angle when changing the sign of the radius.
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Unit 8
Polar Coordinates
A second way to locate a point, and the curves that are far easier to describe in it than in rectangular form.
Lessons and exercises
Lesson 8.2
Conversion
Convert polar to Cartesian using cosine and sine. For the reverse direction, compute the nonnegative radius and choose the angle using the quadrant, not only a tangent ratio. The origin has no unique angle.
Lesson 8.3
Polar Graphs and Symmetry
Read a polar graph by tracking signed radius as the angle changes. Testing substitutions can establish symmetry, but failing one particular test does not prove absence of symmetry because polar representations are not unique.
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