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Sine, Tangent, Cosine Order to 360

Sine, Tangent, Cosine Order to 360
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2018-03-19 15:38
FunctionTrigonometryTransformation
In collections Sine and Cosine Functions
This example demonstrates the changes of sine, tangent, and cosine functions within a 360-degree range. Key mathematical concepts include trigonometric functions and geometric transformations. Using GeoGebra commands such as Shuffle, Element, and Polygon, it dynamically illustrates the periodicity and symmetry of these functions. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Shuffle(list1) → list2
  2. Element(list2, 1) → p
  3. Element(list2, 2) → q
  4. Element(list2, 3) → r
  5. Polygon(A, B, C, D) → q1, a_1, b_1, c_1, d
  6. Polygon(E, F, G, H) → q2, e, f, g, h
  7. Polygon(I, J, K, L) → q3, i, j, k, l
  8. Polygon(M, N, O, P) → q4, m, n, o, p_1
  9. Polygon(Q, R, S, T) → q5, q_1, r_1, s, t
  10. Polygon(U, V, W, Z) → q6, u, v, w, z_1
  11. Polygon(N, A_1, B_1, C_1) → q7, n_1, a_2, b_2, c_2
  12. Polygon(F_1, G_1, S, T) → q9, f_1, g_1, s_1, t_1
  13. Point(xAxis) → I_1
  14. Polygon(Z, W, H_1, I_1) → q10, z_2, w_1, h_1, i_1
  15. Centroid(q1) → D_1
  16. Centroid(q2) → E_1
  17. Centroid(q3) → J_1
  18. IsInRegion(D_1, q4) → da_1
  19. IsInRegion(D_1, q5) → db_1
  20. IsInRegion(D_1, q6) → dc_1
  21. IsInRegion(E_1, q4) → ea_1
  22. IsInRegion(E_1, q5) → eb_1
  23. IsInRegion(J_1, q4) → ja_1
  24. IsInRegion(J_1, q5) → jb_1
  25. IsInRegion(J_1, q6) → jc_1
  26. IsInRegion(E_1, q6) → ec_1

AI Drawing Prompt Reference

Draw a graph showing the changes of sine, tangent, and cosine functions within a 360-degree range, including multiple polygons and points, to dynamically illustrate the periodicity and symmetry of these functions, start by randomly arranging three function values, then represent them with polygons and points, calculate the centroids of the polygons, and finally determine if the centroids are in specific regions, distinguishing them with different colors or styles.
The prompt above was compiled from the original drawing commands and is for reference only.