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Unit Circle Degrees and Radians

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About This MicroSim

Students meet angles twice in this book, speaking two languages: the turtle takes degrees, but math.sin() demands radians. This sim anchors the conversion spatially. Drag the orange point around the unit circle and read the same angle three ways — degrees, radians, and multiples of π — while blue and green projection bars show sin and cos, and a turtle at the center rotates to match the heading.

Learning objective: The student will be able to convert between degrees and radians and locate an angle on the unit circle.

  • Bloom's Taxonomy (2001): Understand → Apply — interpret, convert, use
  • Interaction pattern: direct manipulation (drag the angle point) with live dual readouts and landmark snap buttons

How to Use

  1. Drag the orange point to 180° — the radians readout shows π (about 3.14). A full turn is 2π.
  2. Use the snap buttons to visit the landmark angles and note their radian values (90° = 0.50π, 45° = 0.25π).
  3. Watch the blue sin bar: where is it longest? Where is it zero?
  4. Watch the turtle at the center — its heading is the angle, connecting t.setheading(90) to math.radians(90).

Iframe Embed Code

You can add this MicroSim to any web page by adding this to your HTML:

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<iframe src="https://dmccreary.github.io/learning-python/sims/unit-circle-radians/main.html"
        height="522px"
        width="100%"
        scrolling="no"></iframe>

Lesson Plan

Grade Level

Upper elementary and middle school (ages 10-14), Chapter 18 (Math Module and Turtle Projects)

Duration

10 minutes

Prerequisites

  • Turtle headings in degrees (Chapter 5)
  • math.sin() and math.cos() (Chapter 18)

Activities

  1. Landmark tour (4 min): Students visit each snap angle and record degrees, radians, and the π-multiple in a three-column table.
  2. Sin hunt (3 min): "Drag until sin = 1. Where are you? Drag until sin = 0. How many places can you find?"
  3. Convert by hand (3 min): Students compute radians for 60° using the formula, then verify by dragging.

Assessment

  • Student converts 90°, 180°, and 360° to radians without the sim
  • Student can point to where sin is maximum and where cos is maximum
  • Student can explain why math.sin(90) does not give 1

References

  1. Python Documentation — math.radians — official conversion function
  2. p5.js — the JavaScript library used to build this MicroSim