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Determine which of the following statements are true:  For all polar coordinates, (r,θ)(r,θ) and (r,−θ)(r,-θ) describe the same location.  For all polar coordinates, (r,θ)(r,θ) and (−r,−θ)(-r,-θ) describe the same location.  For all polar coordinates, (r,θ)(r,θ) and (r,θ+2π)(r,θ+2π) describe the same location.  For all polar coordinates, (r,θ)(r,θ) and (−r,θ)(-r,θ) describe the same location.  For all polar coordinates, (−r,θ+π)(-r,θ+π) and (−r,θ−π)(-r,θ-π) describe the same location.  For all polar coordinates, (r,θ)(r,θ) and (−r,θ−π)(-r,θ-π) describe the same location.

Determine which of the following statements are true:  For all polar coordinates, (r,θ)(r,θ) and (r,−θ)(r,-θ) describe the same location.  For all polar coordinates, (r,θ)(r,θ) and (−r,−θ)(-r,-θ) describe the same location.  For all polar coordinates, (r,θ)(r,θ) and (r,θ+2π)(r,θ+2π) describe the same location.  For all polar coordinates, (r,θ)(r,θ) and (−r,θ)(-r,θ) describe the same location.  For all polar coordinates, (−r,θ+π)(-r,θ+π) and (−r,θ−π)(-r,θ-π) describe the same location.  For all polar coordinates, (r,θ)(r,θ) and (−r,θ−π)(-r,θ-π) describe the same location.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.5: Polar Coordinates
Problem 101E
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Question

Determine which of the following statements are true:

  •  For all polar coordinates, (r,θ)(r,θ) and (r,−θ)(r,-θ) describe the same location.
  •  For all polar coordinates, (r,θ)(r,θ) and (−r,−θ)(-r,-θ) describe the same location.
  •  For all polar coordinates, (r,θ)(r,θ) and (r,θ+2π)(r,θ+2π) describe the same location.
  •  For all polar coordinates, (r,θ)(r,θ) and (−r,θ)(-r,θ) describe the same location.
  •  For all polar coordinates, (−r,θ+π)(-r,θ+π) and (−r,θ−π)(-r,θ-π) describe the same location.
  •  For all polar coordinates, (r,θ)(r,θ) and (−r,θ−π)(-r,θ-π) describe the same location.
Expert Solution
Step 1

we have to determine which of the following statements are true:

  •  For all polar coordinates, (r,θ) and (r,−θ) describe the same location.
  •  For all polar coordinates, (r,θ) and (−r,−θ) describe the same location.
  •  For all polar coordinates, (r,θ) and (r,θ+2π) describe the same location.
  •  For all polar coordinates, (r,θ) and (−r,θ) describe the same location.
  •  For all polar coordinates, (−r,θ+π) and (−r,θ−π) describe the same location.
  •  For all polar coordinates, (r,θ) and (−r,θ−π) describe the same location.
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