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Explore Coterminal Angles in Radians

Explore Coterminal Angles in Radians
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2015-01-29 01:45
AngleTrigonometryCoordinate Geometry
This example demonstrates the concept of coterminal angles in radians, helping students understand angle representation in different radian measures. Using commands like GCD, Rotate, and Angle, a series of coterminal angles can be constructed. Suitable for high school mathematics education, particularly in trigonometry and angle conversion.

GeoGebra Commands & Parameters

  1. GCD(a, b) → n
  2. Rotate(B, Deg°, A) → C
  3. Angle(B, A, C) → α
  4. Sequence(Num + i * 2 * Den, 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. CurveCartesian(0.1 * t * cos(t), 0.1 * t * sin(t), t, 6.28319, 2 * π + α) → Spiral1
  10. Textfield(a) → inputBox1
  11. Textfield(b) → inputBox2
  12. Ray(A, B) → Init
  13. Ray(A, C) → Term
  14. Segment(D, E) → i

AI Drawing Prompt Reference

Draw spiral curves representing cosine and sine functions for different periods, starting from a given angle, with three spirals showing variations in cosine and sine functions across cycles, labeled with angles and periods, and include initial and terminal rays in the coordinate system, along with a line segment connecting two points.
The prompt above was compiled from the original drawing commands and is for reference only.