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Ellipse and Trigonometric Functions Construction

Ellipse and Trigonometric Functions Construction
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2021-12-13 00:54
Trigonometry
In collections Open Middle: Distance in the Coordinate Plane
This example demonstrates the relationship between ellipses and trigonometric functions. Key mathematical concepts include ellipses, trigonometric functions, and geometric construction. Using GeoGebra commands such as PointIn, Segment, SurdText, Textfield, Point, If, Mode, Intersect, Polygon, Angle, the construction of ellipses and trigonometric functions is illustrated. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. PointIn(e) → A
  2. PointIn(e) → B
  3. Segment(A, B) → f
  4. SurdText(f) → text1
  5. Textfield(j) → InputBox1
  6. Textfield(k) → InputBox2
  7. Point(Circle[A, sqrt((10 * j) + k)]) → C
  8. Segment(A, C) → l
  9. If(m < i, "Too short!", m > i, "Too long!", "This value is correct!") → text7
  10. Mode(l1) → l2
  11. If(Length[l2] ≟ 0, "No digits repeat!", "Repeated digits exist.") → text8
  12. Intersect(eq1, p) → D
  13. Polygon(A, D, B) → t1, b_1, a_1, d_1
  14. Segment(A, D) → q
  15. Segment(D, B) → r
  16. Angle(B, D, A) → α

AI Drawing Prompt Reference

Draw an ellipse and select two points on it to form a line segment. Display the length of the segment and draw a circle centered at one point on the ellipse with a radius equal to the square root of an input value plus a constant. Check if the line segment connecting a point on the ellipse and a point on the circle meets certain conditions and display appropriate text. Form a polygon using the ellipse and the line segment, and show its properties.
The prompt above was compiled from the original drawing commands and is for reference only.