Transformation of Sine and Cosine Graphs
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This example demonstrates the transformations of sine and cosine graphs including translations and scalings. It involves core math concepts like trigonometric functions, function transformations, amplitude, period, and phase shift. Constructed using GeoGebra objects A (point), B (point), C (point), f (function), text1 (text), and g (function). Suitable for high school mathematics teaching to understand function graph transformation rules.
GeoGebra Commands & Parameters
Numeric A(1.0)Numeric B(1.0)Numeric C(0.0)f(x) = (A * sin(((B * x))°)) + Cg(x) = (A * cos(((B * x))°)) + C
AI Drawing Prompt Reference
Draw the transformation graph of sine and cosine functions. The graph includes three points: A, B, and C, located at (1.0, 1.0), (1.0, 1.0), and (0.0, 0.0) respectively. Additionally, there are two functions: f(x) = A * sin(B*x) + C and g(x) = A * cos(B*x) + C. These functions illustrate function transformation rules such as translations and scalings. By plotting these points and functions, one can intuitively understand the amplitude, period, and phase shift of sine and cosine functions. The construction order is to draw the points first, then the functions.
The prompt above was compiled from the original drawing commands and is for reference only.