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Lesson Worksheet: Polar Coordinates Mathematics • 12th Grade

In this worksheet, we will practice defining and plotting points given in polar coordinates and converting between the Cartesian and polar coordinates of a point.


Consider the points plotted on the graph.

Write down the polar coordinates of 𝐢, giving the angle πœƒ in the range βˆ’πœ‹<πœƒβ‰€πœ‹.

  • Aο€»1,πœ‹4
  • Bο€»βˆ’1,βˆ’πœ‹4
  • Cο€»βˆ’πœ‹4,1
  • Dο€Ό1,7πœ‹4
  • Eο€»1,βˆ’πœ‹4


Identify which of the points plotted on the graph has polar coordinates ο€»1,πœ‹4.

  • A𝐴
  • B𝐢
  • C𝐸
  • D𝐷
  • E𝐡


Which of the ordered pairs (4,βˆ’30)∘, (4,330)∘, (4,390)∘, and (4,βˆ’390)∘ does not describe the position of Point 𝐡 in the diagram?

  • A(4,330)∘
  • B(4,βˆ’390)∘
  • C(4,βˆ’30)∘
  • D(4,390)∘


Which of the ordered pairs ο€»5,πœ‹7, ο€Ό5,15πœ‹7, ο€Ό5,8πœ‹7, and ο€Ό5,βˆ’13πœ‹7 does not describe the position of Point 𝑃 in the diagram?

  • Aο€»5,πœ‹7
  • Bο€Ό5,8πœ‹7
  • Cο€Ό5,βˆ’13πœ‹7
  • Dο€Ό5,15πœ‹7


Find the Cartesian coordinates of the point ο€»1,πœ‹4.

  • Aο€Ώ1,βˆ’βˆš22
  • Bο€Ώβˆš22,√22
  • Cο€Ώ1,√22
  • Dο€Ώβˆš22,πœ‹4
  • Eο€Ώβˆ’βˆš22,βˆ’βˆš22


Given that the polar coordinates of point 𝐴 are (4,120)∘, find the Cartesian coordinates of 𝐴.

  • Aο€»βˆ’2,βˆ’2√3
  • Bο€»2√3,βˆ’2
  • Cο€»2,βˆ’2√3
  • Dο€»βˆ’2,2√3


Convert (2,3) to polar coordinates. Give the angle in degrees and round to one decimal place.

  • A(13.0,56.3)∘
  • B(3.6,56.3)∘
  • C(3.6,33.7)∘
  • D(13.0,33.7)∘


Represent the point with Cartesian coordinates (1,βˆ’1) in terms of polar coordinates.

  • Aο€»βˆš2,πœ‹4
  • Bο€»βˆš2,βˆ’πœ‹4
  • Cο€»βˆ’βˆš2,βˆ’πœ‹4
  • Dο€»2,βˆ’πœ‹4
  • Eο€»βˆ’2,πœ‹4


Convert (βˆ’2,5) to polar coordinates. Give the angle in radians and round to two decimal places.

  • A(29,2.76)
  • B(5.39,1.95)
  • C(5.39,2.76)
  • D(29,1.95)


Find the distance between the polar coordinates (2,πœ‹) and ο€Ό3,βˆ’3πœ‹4. Give your answer accurate to two decimal places.

This lesson includes 30 additional questions and 135 additional question variations for subscribers.

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