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Sin, cos and tan on the unit circle (degrees)

Sin, cos and tan on the unit circle (degrees)
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2013-05-10 11:27
CircleAngleTrigonometryGeometric Construction
This example demonstrates angles on the unit circle, the trigonometric ratios of a given angle, and the relationships between angles. Key math concepts include the unit circle, trigonometric functions, and angle measurement. It is constructed using GeoGebra commands like Point, Arc, Intersect, Segment, and Angle. Suitable for high school mathematics education to help students understand and visualize the basic properties of trigonometric functions.

GeoGebra Commands & Parameters

  1. Point(c) → A
  2. Point(c) → B
  3. Point(c) → C
  4. Point(c) → D
  5. Arc(c, A, B) → quad1
  6. Point(quad1) → P_1
  7. Intersect(xAxis, yAxis) → E
  8. Segment(P_1, E) → a
  9. Angle(P_1, E, A) → α
  10. Segment(P_1, Y_1) → b
  11. Segment(P_1, X_1) → d
  12. Arc(c, B, C) → quad2
  13. Point(quad2) → P_2
  14. Segment(P_2, E) → e
  15. Angle(A, E, P_2) → β
  16. Segment(P_2, X_2) → f
  17. Segment(P_2, Y_2) → g
  18. Arc(c, C, D) → quad3
  19. Point(quad3) → P_3
  20. Segment(P_3, X_3) → h
  21. Segment(P_3, Y_3) → i
  22. Segment(P_3, E) → j
  23. Angle(A, E, P_3) → γ
  24. Arc(c, D, A) → quad4
  25. Point(quad4) → P_4
  26. Segment(P_4, X_4) → k
  27. Segment(P_4, Y_4) → l
  28. Segment(P_4, E) → m
  29. Angle(A, E, P_4) → δ
  30. Point(m) → F
  31. Point(j) → G
  32. Point(e) → H
  33. Point(a) → I
  34. Angle(X_2, E, P_2) → acute_2
  35. Angle(X_3, E, P_3) → acute_3
  36. Angle(P_4, E, X_4) → acute_4

AI Drawing Prompt Reference

Draw a circle and mark four points on it as start, end, and two midpoints, connecting these points with arcs to form four quadrants. Draw coordinate axes at the center of the circle and draw line segments from each point on the circle to the axes, creating multiple segments. Measure and label the angles between these segments and the axes, distinguishing them with different colors. Finally, extend some segments to intersect the axes, creating new intersection points and labeling them.
The prompt above was compiled from the original drawing commands and is for reference only.