MathPlotAI Logo MathPlotAI

Unit Circle and Graphs of Sin, Cos & Tan by GeoGebra Institute of MEI

Unit Circle and Graphs of Sin, Cos & Tan by GeoGebra Institute of MEI
Loading the math board and drawing, please wait…
2015-03-10 18:20
CircleFunctionTrigonometryCoordinate Geometry
This example demonstrates the relationship between the coordinates of a point P on the unit circle and the graphs of sine, cosine, and tangent functions. Core math concepts include the unit circle, trigonometric functions, function graphs, and angle measurement. It uses GeoGebra commands/objects like Intersect, Rotate, Angle, Segment, Midpoint, and Tangent. Suitable for high school students learning about the generation process 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 and plot the graphs of sine, cosine, and tangent functions based on a point P on the circle. Start by drawing the unit circle, then find the intersection point A of the circle and the x-axis, and the origin O. Rotate point A 359.9 degrees around O to get A', and repeat to get A'_1, A'_2, and A'_3. Draw a tangent line from P to the circle, intersecting the x-axis at K, and draw line segment PK. Draw a vertical line from P to the x-axis, intersecting the circle at C, and draw line segment BC. Find the midpoint of BC and draw line segment e, and draw line segment BC. Draw line segment a from (x(P), 0) to P, line segment b from B to P, and line segment d from (θ, 0) to (θ, y(P)).
The prompt above was compiled from the original drawing commands and is for reference only.