MathPlotAI Logo MathPlotAI

Trigonometric Functions on the Unit Circle by Stewart McWilliam

Trigonometric Functions on the Unit Circle by Stewart McWilliam
Loading the math board and drawing, please wait…
2014-01-10 08:21
CircleFunctionTrigonometryCoordinate GeometryGeometric Construction
This example demonstrates how trigonometric functions can be defined on the unit circle, illustrating the geometric meanings of sine, cosine, and tangent functions. Key math concepts include the unit circle, trigonometric function definitions, and trigonometric identities. Construction highlights the use of GeoGebra commands like Intersect, Circle, Segment, Rotate, Angle, Distance, and Midpoint. Suitable for high school mathematics, university preparatory courses, introductory trigonometry teaching, and geometric intuitive understanding.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Circle(A, 1) → c
  3. Segment(A, B) → a
  4. Rotate(B, angle°, A) → B'
  5. Angle(B, A, B') → α
  6. Segment(A, B') → b
  7. Segment(B', C) → d
  8. Distance(C, B') → distanceCB'
  9. Midpoint(C, B') → E
  10. Midpoint(A, C) → D
  11. Segment(A, C) → e
  12. Angle(A, C, B') → β
  13. Angle(B', A, (1, 0)) → γ
  14. Rotate(B, (180 - angle)°, A) → B'_1
  15. Segment(B'_1, B') → n
  16. Segment(A, B'_1) → s
  17. Angle((1, 0), A, B'_1) → δ
  18. Rotate(B, (360 - angle)°, A) → B'_2
  19. Segment(B', B'_2) → t
  20. Segment(A, B'_2) → a_1
  21. Angle((1, 0), A, B'_2) → ε
  22. Intersect(n, yAxis) → I
  23. Rotate((1, 0), (180 + angle)°, A) → J
  24. Segment(A, J) → b_1
  25. Angle((1, 0), A, J) → ζ

AI Drawing Prompt Reference

Draw a unit circle in a coordinate system, mark the intersection point with the x-axis, and draw a radius from this point to the circle. Rotate this radius by an angle around the origin and mark the rotated radius and its angle with the x-axis. Indicate the corresponding cosine and sine values on the circle and draw the corresponding function segments. Finally, show the construction of the tangent line and label all angles and segments.
The prompt above was compiled from the original drawing commands and is for reference only.