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Trigonometric Functions of Regular Polygons

Trigonometric Functions of Regular Polygons
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2015-12-19 18:23
CirclePolygonFunctionTrigonometry
This example demonstrates the relationship between regular polygons and circles. By constructing regular polygons and increasing the number of sides infinitely, the polygon approaches a circle. Trigonometric functions are defined as the lengths of various line segments. Using GeoGebra commands such as Point, Circle, Intersect, Polygon, Rotate, etc., the properties of regular polygons can be dynamically demonstrated. Suitable for high school mathematics education, particularly for learning trigonometric functions and geometric construction.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Circle(A, 1) → c
  3. Intersect(c, xAxis, 2) → B
  4. Circle(B, (2 * sin(π / n))) → d
  5. Intersect(c, d, 1) → C
  6. Polygon(B, C, n) → poly1, a, l, m, p, q, r, s, t_2, a_1, b_1, c_1, b, d_1, e_1, f_1, g_1, h_1, i_1, j_1, k_1, l_1, m_1, e, n_1, p_1, q_1, r_1, s_1, t_1, a_2, b_2, c_2, d_2, f, e_2, f_2, g_2, h_2, i_2, j_2, k_2, l_2, m_2, n_2, g, p_2, D, E, F, G, H, I, J, K, L, h, M, N, O, P, Q, R, S, T, U, V, i, W, Z, A_1, B_1, C_1, D_1, E_1, F_1, G_1, H_1, j, I_1, J_1, K_1, L_1, M_1, N_1, O_1, P_1, Q_1, R_1, k, S_1, T_1, U_1, V_1, W_1, Z_1, A_2, B_2, C_2
  7. Rotate(B, t, A) → B'
  8. Angle(B, A, B') → α
  9. Segment(A, B') → q_2
  10. Intersect(q_2, poly1) → D_2
  11. Rotate(B, t + 90°, A) → B'_1
  12. Angle(B, A, B'_1) → β
  13. Segment(A, B'_1) → a_3
  14. Intersect(a_3, poly1) → G_2
  15. Segment(A, B'_1) → b_3
  16. Intersect(b_3, poly1) → H_2