Polar Graphing Worksheets Grade 12

Trigonometry

Polar Coordinate System

Each printable worksheet below is a full page of practice problems and comes with an answer key that explains how to solve every problem, step by step. Open a worksheet and use the Print / Save as PDF button to download it.

Worksheet 1

9 problems
  1. ∫(x³ - 3x² + 2x) dx from 0 to 2 = ?
  2. Graph r = 5 + 5cos(θ) and identify the shape.
  3. ∫(x²e^x) dx from 0 to 1 = ?

…and 6 more problems

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Worksheet 2

9 problems
  1. ∫(x³ - 2x² + 5) dx from -1 to 2 = ?
  2. Graph r = 7 + 7sin(θ) and identify the shape.
  3. Mia is tracking the orbit of a satellite using polar coordinates. The satellite's trajectory is modeled by the polar equation r = 13 + 10cos(θ). If the satellite reaches its closest point to Earth when θ = π, what is that minimum distance r from Earth's center?

…and 6 more problems

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Worksheet 3

9 problems
  1. Ben is an astronomer studying the orbit of a comet. The comet's path relative to the sun at the origin is approximated by the polar equation r = 6 / (1 + 3 cos θ). What type of conic section does this represent, and what is the eccentricity?
  2. ∫(x²e^(x³)) dx from 0 to 1 = ?
  3. Graph r = 5 + 3cos(θ) and identify the shape.

…and 6 more problems

Open & Print Worksheet 3

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