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Addition Formula Template: Geometric Demonstration with Quadrilaterals and Linea

Addition Formula Template: Geometric Demonstration with Quadrilaterals and Linea
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2019-01-24 05:26
PolygonAngleFunctionGeometric ConstructionSlider Animation
① This example dynamically demonstrates the geometric meaning of addition formulas (e.g., sine/cosine of sum of angles) within the context of quadrilaterals and linear regression. ② Core mathematical concepts include addition formulas, quadrilateral properties, linear regression, arithmetic operations, difference of squares, slope, and angle relationships. ③ Construction details: Uses GeoGebra commands Point, Intersect, Segment, OrthogonalLine, Polygon, and Angle; objects include points A, B, C, D, E, F, G, lines f, h, i, g, j, polygon q1, auxiliary lines g_1, e, f_1, b, t1, d, b_1, a, and angles α, β with text1. ④ Suitable for high school or early college students to explore geometric derivations of addition formulas, slope connections in linear regression, and dynamic parameter adjustments for visual learning, serving as a teaching demonstration or inquiry-based tool.

GeoGebra Commands & Parameters

  1. Point(c) → A
  2. Intersect(xAxis, yAxis) → B
  3. Segment(B, A) → f
  4. Segment(A, C) → h
  5. OrthogonalLine(B, h) → i
  6. Intersect(i, h) → D
  7. Point(j) → E
  8. Intersect(j, xAxis) → F
  9. Point(yAxis) → G
  10. Polygon(G, E, F, B) → q1, g_1, e, f_1, b
  11. Polygon(B, A, D) → t1, d, b_1, a
  12. Angle(A, D, B) → α
  13. Angle(D, F, B) → β

AI Drawing Prompt Reference

Create a dynamic geometric diagram illustrating the geometric meaning of sine and cosine addition formulas. Include a quadrilateral formed by two points on the coordinate axes, a point on a slanted line, and the intersection of that line with the x-axis. Also include a right triangle with vertices at the origin, the point on the slanted line, and the foot of the perpendicular from the origin to that line. Mark two key angles: one at the foot of the perpendicular, and another at a vertex of the quadrilateral. The diagram should show relationships among slopes, angles, and linear regression, with adjustable parameters via sliders.
The prompt above was compiled from the original drawing commands and is for reference only.