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Points, Vectors, and Functions

Points, Vectors, and Functions

Translating Equations and Inequalities between Coordinate Systems Exercises

Example 1

  • Translate each equation into polar coordinates.
  1. (x + 2)2 + (y + 2)2 = 4
  2. x + y2 = 0
  3. (x + y)2 = 4

Example 2

  • Translate each inequality into polar coordinates.
  1. y ≥ 5
  2. x + y ≤ 3
  3. x2 + y2 < 100

Example 3

  • Translate each equation into rectangular coordinates.
  1. r cos θ + r2 sin2 θ = 4r sin θ
  2. r = 4

Example 4

  • Translate each inequality into rectangular coordinates. Assume r is non-negative.
  1. r cos2 θ + r sin2 θ = 1
  2. 5r2 cos2 θ + 10r cos θ + 5 – 4r2 sin2 θ + 16r sin θ – 16 = 20
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