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Explore Coterminal Angles (in degrees)

Explore Coterminal Angles (in degrees)
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2015-01-29 01:42
AngleTrigonometryCoordinate Geometry
This example demonstrates the concept of coterminal angles using degrees. It uses commands like Rotate, Angle, and Ray to draw multiple coterminal angles, helping to understand the periodicity of angles. Suitable for high school mathematics, particularly trigonometry and geometric construction.

GeoGebra Commands & Parameters

  1. Rotate(B, θ * π / 180, A) → C
  2. Angle(B, A, C) → α
  3. Ray(A, B) → a
  4. Sequence(α * 180 / π + i * 360, i, 2, -2, -1) → list1
  5. CurveCartesian(0.1 * t * cos(t), 0.1 * t * sin(t), t, 6.28319, 2 * π + α + 2 * π) → Spiral2
  6. CurveCartesian(0.1 * t * cos(t), 0.1 * t * sin(t), t, 6.28319, 2 * π + α + 4 * π) → Spiral3
  7. CurveCartesian(0.1 * t * cos(t), -0.1 * t * sin(t), t, 6.28319, 2 * π - β * π / 180) → Spiral4
  8. CurveCartesian(0.1 * t * cos(t), -0.1 * t * sin(t), t, 6.28319, 2 * π - (β - 360) * π / 180) → Spiral5
  9. Textfield(θ) → θ_1
  10. Ray(A, C) → b
  11. CurveCartesian(0.1 * t * cos(t), 0.1 * t * sin(t), t, 6.28319, 2 * π + α) → Spiral1

AI Drawing Prompt Reference

Draw an angle with vertex at the origin, initial side along the positive x-axis, and terminal side determined by an adjustable angle value. Show this angle and all its coterminal angles (differing by multiples of 360 degrees), marking each terminal side with a ray. Use spiral curves to illustrate the periodic extension of angles. Label the angle measure and provide an input field to adjust the angle.
The prompt above was compiled from the original drawing commands and is for reference only.