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Worksheet: Conversion between Rectangular and Polar Equations

Q1:

Consider the Cartesian equation 𝑦 = 2 π‘₯ + 3 .Complete the following steps to find the polar form of the equation by writing an equivalent equation each time.

First, use the fact that π‘₯ = π‘Ÿ πœƒ c o s to eliminate π‘₯ .

  • A 𝑦 = π‘Ÿ πœƒ + 3 c o s
  • B 𝑦 = 2 ( π‘Ÿ πœƒ + 3 ) c o s
  • C 𝑦 = 2 π‘Ÿ πœƒ c o s
  • D 𝑦 = 2 π‘Ÿ πœƒ + 3 c o s
  • E 𝑦 = 2 π‘Ÿ πœƒ βˆ’ 3 c o s

Now, use the fact that 𝑦 = π‘Ÿ πœƒ s i n to eliminate 𝑦 .

  • A π‘Ÿ πœƒ = 2 π‘Ÿ πœƒ + 3 s i n c o s
  • B π‘Ÿ πœƒ = 2 π‘Ÿ πœƒ s i n c o s
  • C π‘Ÿ πœƒ = 2 ( π‘Ÿ πœƒ + 3 ) s i n c o s
  • D π‘Ÿ πœƒ = π‘Ÿ πœƒ + 3 s i n c o s
  • E π‘Ÿ πœƒ = 2 π‘Ÿ πœƒ βˆ’ 3 s i n c o s

Finally, make π‘Ÿ the subject.

  • A π‘Ÿ = βˆ’ 3 πœƒ βˆ’ 2 πœƒ s i n c o s
  • B π‘Ÿ = 3 πœƒ + 2 πœƒ s i n c o s
  • C π‘Ÿ = 3 πœƒ βˆ’ 2 πœƒ s i n c o s
  • D π‘Ÿ = 3 πœƒ βˆ’ πœƒ s i n c o s
  • E π‘Ÿ = 3 πœƒ + πœƒ s i n c o s

Q2:

Convert the equation π‘₯ + 𝑦 = 2 5 2 2 into polar form.

  • A π‘Ÿ = 2 5 2
  • B π‘Ÿ = 2 5
  • C π‘Ÿ = 5 0
  • D π‘Ÿ = 5
  • E π‘Ÿ = 6 2 5