Graph of Sine and Cosine with Perimeters

Graph of Sine and Cosine with Perimeters
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2019-11-14 00:10
This example demonstrates the graphing of sine and cosine functions along with the calculation of their perimeters. Key math concepts include trigonometric functions, function graphs, coordinate geometry, and perimeter computation. GeoGebra commands and objects used in the construction are Intersect, Extremum, and various points and parameters like k_2, c_2, b_2, a_2, k, c, b, a, d, e, h, f, A, B, C, D, E, F, G, H, I, J, K, L, M, g, H_1, I_1, J_1, K_1, L_1, M_1, T, U, V, W, Z, A_1, P_2, Q_2. Suitable for high school students learning trigonometry and coordinate geometry, this example aids in understanding function graphs and geometric properties.

GeoGebra Commands & Parameters

  1. Intersect(f, h, -20, 20) → A, B, K, L, M, , , , , , , , C, , , , , , , , , , , D, , , E, F, G, H, I, J
  2. Intersect(g, h, -20, 20) → H_1, I_1, Z, A_1, , , , , , , , , J_1, , , , , , , , , , , K_1, , , L_1, M_1, T, U, V, W
  3. Extremum(f, -20, 20) → P_2, Q_2, R, S, , , , , , , , , R_2, , , , , , , , , , , S_2, , , T_2, U_2, N, O, P, Q
  4. Extremum(g, -20, 20) → Z_3, A_4, E_1, F_1, G_1, , , , , , , , B_4, , , , , , , , , , , C_4, , , D_4, E_4, F_4, B_1, C_1, D_1