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Unit Circle and Sine Graph by Emily Young

Unit Circle and Sine Graph by Emily Young
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2019-09-14 05:13
CircleFunctionTrigonometryCoordinate GeometryGeometric Construction
This example demonstrates how to generate the sine graph from the unit circle. It involves core mathematical concepts such as the unit circle, trigonometric functions, and the sine function. Construction highlights the use of GeoGebra commands and objects like Point, Rotate, Angle, Function, Segment, Circle, Vector, and Sequence. Suitable for high school students learning trigonometric functions 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 with its center on the left side of the coordinate plane)Skip. From the center, draw a horizontal ray to the left. Place a moving point on the circle that rotates by an angle parameter. Connect the center to this point with a radius segment, and mark the angle. Drop a perpendicular from the moving point to the horizontal axis. On the right, set up a coordinate system with the horizontal axis representing angle and the vertical axis representing sine. Map the y-coordinate of the moving point to the sine curve, creating a corresponding point. Connect the moving point to this mapped point with a segment to show the generation of the sine graph. Add tick marks on both axes and draw a portion of the sine curve.
The prompt above was compiled from the original drawing commands and is for reference only.