正弦与余弦函数变换(2):动态演示
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本范例演示正弦与余弦函数的振幅变化和垂直平移。通过动态可修改的图形,帮助理解函数变换的概念。使用了Dilate(放大)、Distance(距离)、Vector(向量)、Translate(平移)、Mirror(镜像)等GeoGebra命令。适合高中数学教学和学习。
GeoGebra 命令及参数
Dilate(V, If[3 < j ≤ 4, 4 - j, 0], A_1) → V'_1Distance((0, 0), V'_1) → a_2Vector(A, B) → vDilate(F, If[0 < j ≤ 1, 1 - j, 0], G) → F'Dilate(K, If[1 < j ≤ 2, 2 - j, 0], L) → K'Vector(K, K') → wDistance(K, L) → distanceKLDilate(H, If[3 < j ≤ 4, 4 - j, 0], D) → H'Distance(M, H') → kVector(M, H') → lDistance(M, H') → distanceMH'Dilate(M, If[5 < j ≤ 6, 6 - j, 0], P) → M'Vector(M, M') → mTranslate(f_1, m) → g_1Vector(O, N) → u_1Distance(O, N) → distanceONMirror(r, y = 0) → r_1Mirror(s, y = 0) → s_1Mirror(t, y = 0) → t_1Mirror(H, y = 0) → H'_1Mirror(I, y = 0) → I'Mirror(K', y = 0) → K''Vector(K, K'') → uDistance(K, K'') → distanceKK''Distance(K, K'') → bDilate(H'_1, If[3 < j ≤ 4, 4 - j, 0], E) → H''Distance(M, H'') → oVector(M, H'') → v_1Distance(M, H'') → a_1Distance(M, H'') → distanceMH''Translate(h_1, m) → p_1Vector(O, Q) → w_1Distance(O, Q) → distanceOQDilate(W, If[1 < j ≤ 2, 2 - j, 0], V) → W'Vector(W, W') → c_1Distance(W, V) → distanceWVMirror(q_1, y = 0) → d_1Mirror(f_2, y = 0) → e_1Mirror(g_2, y = 0) → i_1Mirror(W', y = 0) → W''Vector(W, W'') → j_1Distance(Z, W) → distanceZWDilate(Z, If[3 < j ≤ 4, 4 - j, 0], A_1) → V'Mirror(V', y = 0) → V''Distance(W, V') → k_1Vector(C_1, D_1) → l_1Vector(C_1, E_1) → m_1Distance(C_1, D_1) → distanceC1D1Distance(C_1, E_1) → distanceC1E1Distance(V, V'_1) → o_1Dilate(D_1, If[5 < j ≤ 6, 6 - j, 0], G_1) → H_1Vector(D_1, H_1) → u_2Translate(C_1, u_2) → I_1Distance(I_1, H_1) → distanceI1H1Translate(h_2, u_2) → q_2Vector(I_1, H_1) → v_2Dilate(E_1, If[5 < j ≤ 6, 6 - j, 0], J_1) → K_1Vector(E_1, K_1) → w_2Translate(C_1, w_2) → L_1Translate(p_2, w_2) → r_2Vector(L_1, K_1) → b_2Distance(L_1, K_1) → distanceL1K1Textfield(a) → InputBox1Textfield(d) → InputBox2
AI 绘图提示语参考
绘制正弦和余弦函数的振幅变化和垂直平移动态演示。首先绘制正弦和余弦函数图,然后通过放大或缩小改变振幅,再通过平移和镜像变换进行垂直平移。最后,通过一系列变换操作,动态展示函数的变换过程。
以上提示语为根据原始绘图命令整理而来,仅供参考。