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Lesson: Conversion between Rectangular and Polar Equations

In this lesson, we will learn how to convert equations from polar to rectangular form.

Worksheet • 2 Questions

Q1:

Consider the polar equation π‘Ÿ = 2 πœƒ c o s . Complete the following steps to help you find the Cartesian form of the equation by writing an equivalent equation each time.

Multiply both sides of the equation through by π‘Ÿ .

  • A π‘Ÿ = 2 π‘Ÿ πœƒ 2 c o s
  • B π‘Ÿ = π‘Ÿ πœƒ c o s
  • C π‘Ÿ = 2 πœƒ 2 c o s
  • D π‘Ÿ = 2 π‘Ÿ πœƒ c o s
  • E π‘Ÿ = π‘Ÿ πœƒ 2 c o s

Use the fact that π‘₯ = π‘Ÿ πœƒ c o s to simplify the expression.

  • A π‘Ÿ = 2 π‘₯ 2
  • B 2 π‘Ÿ = π‘₯ 2
  • C π‘Ÿ = π‘₯ 2
  • D π‘Ÿ = π‘₯
  • E π‘Ÿ = 2 π‘₯

Given that π‘₯ = π‘Ÿ πœƒ c o s and 𝑦 = π‘Ÿ πœƒ s i n , we can use the Pythagorean theorem to show that π‘₯ + 𝑦 = π‘Ÿ 2 2 2 . Use this to eliminate the π‘Ÿ 2 in the previous expression.

  • A π‘₯ + 𝑦 = 2 π‘₯ 2 2
  • B π‘₯ + 𝑦 = π‘₯ 2 2 2
  • C π‘₯ + 𝑦 = π‘₯ 2 2
  • D π‘₯ + 𝑦 = π‘₯ 2 2 2
  • E π‘₯ + 𝑦 = 4 π‘₯ 2 2 2

Q2:

Convert π‘Ÿ = 2 πœƒ s e c into cartesian form.

  • A π‘₯ = 2
  • B π‘₯ = 4
  • C 𝑦 = 2
  • D 𝑦 = 2 2
  • E π‘₯ = 2 2
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