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Points, Vectors, and Functions

Points, Vectors, and Functions

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. %Graph the region being described by the inequality.
  1. y ≥ 5
  2. x + y≤ 3
  3. x2 + y2 < 100

Example 3

  • Translate each equation into rectangular coordinates.
  1. rcosθ + r2sin2θ = 4rsinθ
  2. (hint: multiply through by r)
  3. r = 4 (hint: square both sides.)

Example 4

  • Translate each inequality into rectangular coordinates. Assume r is non-negative.%Graph the region being described by the inequality.
  1. sin θ < 1/r
  2. rcos2θ + rsin2θ = 1
  3. 5r2cos2θ + 10rcosθ + 5 -4r2sin2θ + 16rsinθ-16 = 20
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