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Unit Circle and Tangent Graph by Anthony OR 柯志明

Unit Circle and Tangent Graph by Anthony OR 柯志明
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2012-04-17 20:51
CircleFunctionTrigonometryGeometric Construction
In collections Trigonometric Graphs and the Unit Circle Trigonometric Graphs and the Unit Circle wellington point The Unit Circle Begins Trigonometric Graphs and the Unit Circle Trigonometric Graphs
This example demonstrates the graphs of cosine and tangent functions using the unit circle. Key mathematical concepts include trigonometry, unit circle, angles, and coordinate transformations. Construction involves GeoGebra commands such as Point, Rotate, Segment, Angle, Circle, and Vector. Suitable for high school students learning trigonometric basics or for mathematical teaching demonstrations.

GeoGebra Commands & Parameters

  1. Point(Ray[(0, 0), (-1, 0)]) → B
  2. Rotate(A, θ, B) → P
  3. Segment(A, Intersect[Line[B, P], x = x(A)]) → h
  4. Segment(P, Intersect[Line[B, P], x = x(A)]) → g
  5. Rotate(A, θ, B) → A'
  6. Angle(A, B, A') → α
  7. Rotate(A, θ, B) → A'_1
  8. Angle(A, B, A'_1) → β
  9. Segment(Q, (x(Q), 0)) → e
  10. Circle(B, A) → c
  11. Segment(B, P) → a
  12. Vector((x(B), y(Corner[1])), (x(B), y(Corner[4]))) → u
  13. Vector((0, y(Corner[1])), (0, y(Corner[4]))) → w
  14. Vector((0, 0), (x(Corner[2]), 0)) → z
  15. Sequence(Segment[((0.75 * i), 0), ((0.75 * i), -0.025)], i, 1, 4) → list1
  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. Sequence(Segment[B + ((0.5 * i) - 1, 0), B + ((0.5 * i) - 1, -0.025)], i, 0, 4) → list4
  20. Segment(C, Q) → d
  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

AI Drawing Prompt Reference

Draw a unit circle and demonstrate the cosine and tangent functions by showing angles and their corresponding coordinates. Rotate a point around the origin along the circle, connecting it to the x-axis to form the sine and cosine waves. Include tangent lines and label the angles and transformations to illustrate the trigonometric concepts for high school teaching.
The prompt above was compiled from the original drawing commands and is for reference only.