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Graphing Sine and Cosine Functions by mathspace

Graphing Sine and Cosine Functions by mathspace
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2022-08-14 21:57
VectorFunctionTrigonometryCoordinate GeometryGeometric Construction
This example demonstrates how to graph sine and cosine functions using the unit circle. Key math concepts include the unit circle, trigonometric functions, coordinate geometry, and vectors. Construction highlights include GeoGebra commands like Point, Rotate, Angle, Function, Segment, Circle, Vector, Sequence, AngularBisector, and Intersect. 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((0.009996343636607063, 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
  27. Point(list3) → C
  28. Circle(C, 0.3) → g
  29. AngularBisector(A, B, A') → h
  30. Intersect(g, h, 2) → D

AI Drawing Prompt Reference

Draw the graphs of sine and cosine functions based on the unit circle. Start by drawing the unit circle and point B on the x-axis. Rotate point A to generate points P and A', and calculate angles α and β. Then, draw the sine function graph f from point Q to the x-axis, and the unit circle c. Construct line segment a from point B to P, and vectors u, w, and z. Draw a series of horizontal line segments from the origin and vertical line segments from point B. Finally, draw the cosine function graph, including line segment d from point P to Q.
The prompt above was compiled from the original drawing commands and is for reference only.