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Tracing Sine Ratios in a Unit Circle

Tracing Sine Ratios in a Unit Circle
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2017-05-18 15:48
CircleFunctionTrigonometryCoordinate Geometry
This example demonstrates the tracing of sine ratios in a unit circle. The math concepts involved include circle, trigonometry, sine ratios, and unit circle. It is constructed using GeoGebra commands such as Point, Rotate, Angle, Function, Segment, Circle, Vector, Sequence, etc. Suitable for high school students learning trigonometry and analytical geometry.

GeoGebra Commands & Parameters

  1. Point(Ray[(0, 0), (-1, 0)]) → B
  2. Rotate(A, θ, B) → P
  3. Rotate(A, θ, B) → A'
  4. Angle(A, B, A') → α
  5. Rotate(A, θ, B) → A'_1
  6. Angle(A, B, A'_1) → β
  7. Function(sin((120° * x)), 0, x(Q)) → f
  8. Segment(Q, (x(Q), 0)) → e
  9. Circle(B, A) → c
  10. Segment(B, P) → a
  11. Vector((x(B), y(Corner[1])), (x(B), y(Corner[4]))) → u
  12. Vector((0, y(Corner[1])), (0, y(Corner[4]))) → w
  13. Vector((0, 0), (x(Corner[2]), 0)) → z
  14. Sequence(Segment[((0.75 * i), 0), ((0.75 * i), -0.025)], i, 1, 4) → list1
  15. Segment(P, (x(P), 0)) → b
  16. Vector(B - (1.2, 0), B + (1.2, 0)) → v
  17. Sequence(Segment[(0, (0.5 * i) - 1), (-0.025, (0.5 * i) - 1)], i, 0, 4) → list2
  18. Sequence(Segment[(x(B), (0.5 * i) - 1), (x(B) - 0.025, (0.5 * i) - 1)], i, 0, 4) → list3
  19. Segment(P, Q) → d
  20. Sequence(Segment[B + ((0.5 * i) - 1, 0), B + ((0.5 * i) - 1, -0.025)], i, 0, 4) → list4
  21. Point(Ray[(0, 0), (-1, 0)]) → B_1
  22. Rotate(A_1, θ, B_1) → P_1
  23. Rotate(A_1, θ, B_1) → A'_2
  24. Rotate(A_1, θ, B_1) → A'_3
  25. Circle(B_1, A_1) → c_1
  26. Segment(B_1, P_1) → a_1

AI Drawing Prompt Reference

Draw a unit circle and demonstrate the sine ratio within it. Start by drawing a ray from the origin to the left side of the circle, then rotate this ray by an angle to get a point, and rotate again to get another point, connecting them to form a line segment. Inside the circle, plot a function based on the sine of the rotation angle and connect the point to the bottom of the circle to show the sine ratio. Add some helper line segments and vectors to clearly illustrate the connection between trigonometric functions and the unit circle.
The prompt above was compiled from the original drawing commands and is for reference only.