Worksheet: Graphing Polar Curves

In this worksheet, we will practice plotting and drawing graphs of equations in polar form and identifying classical shapes in polar form such as circles, cardioids, and roses.

Q1:

Select the graph of 𝑟=4(3𝜃)cos.

  • A
  • B
  • C
  • D

Q2:

Select the graph of 𝑟=32(𝜃)cos.

  • A
  • B
  • C
  • D

Q3:

The figure shows the spiral 𝑟=𝜃.

What is the range of the parameter 𝜃? Give your answer in terms of 𝜋.

  • AIt cannot be determined from this graph.
  • B0𝜃13𝜋2
  • C0𝜃7𝜋2
  • D0𝜃𝜋
  • E0𝜃13𝜋4

Q4:

Select the equation that represents the given graph.

  • A𝑟=36(2𝜃)cos
  • B𝑟=6(2𝜃)cos
  • C𝑟=36(2𝜃)sin
  • D𝑟=36(2𝜃)cos
  • E𝑟=6(2𝜃)sin

Q5:

Select the equation that represents the given graph.

  • A𝑟=2(𝜃)cos
  • B𝑟=1+2(𝜃)sin
  • C𝑟=1+2(𝜃)cos
  • D𝑟=2(𝜃)sin
  • E𝑟=12(𝜃)cos

Q6:

The following graph is called a rose graph.

Which of the following is its polar equation?

  • A𝑟=(3𝜃)sin
  • B𝑟=2(3𝜃)cos
  • C𝑟=(3𝜃)cos
  • D𝑟=2(3𝜃)sin
  • E𝑟=2(𝜃)sin

Q7:

Which of the following is the polar equation of the given graph?

  • A𝑟=2(𝜃)cos
  • B𝑟=(𝜃)sin
  • C𝑟=2
  • D𝑟=(𝜃)cos
  • E𝑟=2(𝜃)sin

Q8:

The following graph is called a lemniscate.

Which of the following is its polar equation?

  • A𝑟=4(2𝜃)cos
  • B𝑟=(2𝜃)cos
  • C𝑟=4(2𝜃)cos
  • D𝑟=4(2𝜃)sin

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