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Unit Circle and Graphs of Sin, Cos & Tan

Unit Circle and Graphs of Sin, Cos & Tan
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2020-03-06 01:19
CircleFunctionTrigonometryGeometric ConstructionGraphing
This example demonstrates the relationship between the coordinates of point P on the unit circle and the graphs of sine, cosine, and tangent functions. It involves core mathematical concepts such as the unit circle, trigonometric function definitions, and function graph plotting. The construction uses GeoGebra commands like Intersect, Rotate, Angle, Segment, Midpoint, and Tangent, with objects including circle, angle θ, points A/B/P, angles α/β/γ, function f, points A'/A'_1/A'_2/A'_3, angles δ/ε, lengths a/b/d/s, and text elements. It is suitable for high school students learning about the origin and properties of trigonometric function graphs.

GeoGebra Commands & Parameters

  1. Intersect(circle, xAxis, 2) → A
  2. Intersect(xAxis, yAxis) → B
  3. Rotate(A, θ°, B) → P
  4. Angle(A, B, P) → α
  5. Angle(P, B, A) → β
  6. Rotate(A, 359.9°, B) → A'
  7. Angle(A, B, A') → γ
  8. Rotate(A, 359.9°, B) → A'_1
  9. Rotate(A, 359.9°, B) → A'_2
  10. Angle(A, B, A'_2) → δ
  11. Rotate(A, 359.9°, B) → A'_3
  12. Angle(A, B, A'_3) → ε
  13. Segment((x(P), 0), P) → a
  14. Segment(B, P) → b
  15. Segment((θ, 0), (θ, y(P))) → d
  16. Midpoint(C, P) → D
  17. Midpoint(E, F) → G
  18. Segment(B, C) → e
  19. Midpoint(B, C) → H
  20. Segment(E, I) → h
  21. Midpoint(E, I) → J
  22. Tangent(P, circle) → k,
  23. Intersect(k, xAxis) → K
  24. Segment(P, K) → l
  25. Midpoint(K, P) → L
  26. Segment(E, M) → m
  27. Midpoint(M, E) → N

AI Drawing Prompt Reference

Draw a unit circle with a point P on it. Connect P to the center of the circle and mark its projection on the x-axis. At the center, draw an angle θ, rotate P around the center by θ to get point P, and label angles α and β. Create three points A', A'_1, and A'_2 near the center with angles slightly different from θ, and label angles γ, δ, and ε. Draw the perpendicular segment from P to the x-axis and the segment from P to center B. Find the midpoint D on the perpendicular segment and draw segment d. Draw the tangent line at P, find its intersection with the x-axis at K, connect P to K, and find the midpoint L.
The prompt above was compiled from the original drawing commands and is for reference only.