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Unit Circle and Trigonometric Functions Demo

Unit Circle and Trigonometric Functions Demo
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2018-12-10 22:52
CircleTrigonometryCoordinate GeometryGeometric Construction
This example demonstrates the relationship between the unit circle and trigonometric functions, visually showing how angles correspond to sine and cosine values. Core math concepts include the unit circle, trigonometric functions (sine, cosine), angles, and right triangles. GeoGebra commands and objects used in construction are Circle, Point, Rotate, Angle, Segment, OrthogonalLine, Polygon, Slope, and Line. Suitable for high school mathematics teaching to help students intuitively understand the definitions and properties of trigonometric functions.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A_1
  2. Circle(A_1, r) → c
  3. Point(xAxis) → B
  4. Rotate(B, α_1, A_1) → B'
  5. Angle(B, A_1, B') → α
  6. Segment(B', A_1) → a
  7. Intersect(c, a, 1) → C
  8. Segment(A_1, C) → b
  9. OrthogonalLine(C, yAxis) → d
  10. Intersect(d, yAxis) → O
  11. OrthogonalLine(C, xAxis) → e
  12. Intersect(e, xAxis) → A
  13. OrthogonalLine(C, xAxis) → f
  14. Intersect(f, xAxis) → D
  15. Polygon(A_1, C, D) → poly1, d_1, a_1, c_1
  16. OrthogonalLine(C, b) → g
  17. Slope(g) → m
  18. Line(A_1, C) → j
  19. Intersect(c, xAxis, 2) → F
  20. OrthogonalLine(F, xAxis) → k
  21. Intersect(j, k) → G
  22. Polygon(A_1, G, F) → poly2, f_1, a_2, g_1
  23. Segment(G, F) → l

AI Drawing Prompt Reference

Draw a unit circle and mark a point on it. Draw a line segment from the point to the center of the circle. Rotate the point around the center by a certain angle and draw the rotated point and line. Find the intersection point on the circle with the rotated line and draw perpendicular lines from this point to the coordinate axes to form a right triangle. Finally, represent the triangle and the rotated part as polygons and show the intersection points of the perpendicular lines.
The prompt above was compiled from the original drawing commands and is for reference only.