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Sine Cosine Tangent to 90

Sine Cosine Tangent to 90
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2018-03-19 15:37
AngleFunctionTrigonometryGeometric Construction
In collections Right Angled Triangles
This example demonstrates the behavior and relationships among sine, cosine, and tangent functions within the range of 0 to 90 degrees. Key math concepts include trigonometric definitions, unit circle, and right triangle side-angle relationships. GeoGebra commands like Shuffle, Element, Polygon, Point, Centroid, and IsInRegion are used to create dynamic visualizations and interactions. Suitable for high school mathematics education to help students intuitively grasp the properties and geometric significance of trigonometric functions.

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 relationships and behaviors of sine, cosine, and tangent functions within the range of 0 to 90 degrees. Include a unit circle and right triangles to help understand the geometric significance and properties of trigonometric functions. Start by creating multiple polygons to represent the values of trigonometric functions at different angles, then mark key points on the unit circle and calculate the centroids of the polygons. Finally, determine if the centroids are within other polygons to illustrate the relationships between function values.
The prompt above was compiled from the original drawing commands and is for reference only.