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Symmetry, Translation, Rotation of sin, tan Functions

Symmetry, Translation, Rotation of sin, tan Functions
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2018-07-01 20:06
FunctionTrigonometryTransformation
This example demonstrates the symmetry, translation, and rotation transformations of sine and tangent functions. It involves core math concepts like symmetry, translation, rotation, trigonometric function graphs, and derivatives. Constructed using GeoGebra commands: Circle, Point, Vector, Translate, Mirror. Suitable for high school mathematics teaching and learning function transformations.

GeoGebra Commands & Parameters

  1. Circle(A, 4) → c
  2. Point(c) → B
  3. Vector(A, B) → u
  4. Translate(g, u) → g_1
  5. Mirror(g_1, xAxis) → a
  6. Mirror(g, xAxis) → g_2
  7. Mirror(f, yAxis) → f_1

AI Drawing Prompt Reference

Draw the graphs of sine and tangent functions to demonstrate their symmetry, translation, and rotation transformations. Start by drawing a circle and taking one point as the starting point of a translation vector, then another point on the circle as the endpoint to generate the translation vector. Translate the sine function graph, then mirror the translated graph to the x-axis. Mirror the original sine function graph to the x-axis, and mirror the tangent function graph to the y-axis.
The prompt above was compiled from the original drawing commands and is for reference only.