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Small Angle Limits

Small Angle Limits
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2019-11-04 06:33
CircleTrigonometryCalculusLimitGeometric Construction
This example demonstrates the relationship between a circle's tangent and arc under small angles, dynamically verifying the concept of limits. Core math concepts include limits, circles, tangents, and trigonometry. GeoGebra commands used are Intersect, Circle, Point, Tangent, Segment, CircleArc, and Angle. Suitable for high school and above students learning calculus and geometric constructions.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → O
  2. Circle(O, 1) → c
  3. Point(c) → A
  4. Tangent(A, c) → f,
  5. Point(f) → C
  6. Segment(C, O) → g
  7. Segment(O, A) → h
  8. Intersect(c, g, 1) → B
  9. CircleArc(O, A, B) → d
  10. Segment(C, A) → i
  11. Angle(C, A, O) → α
  12. Angle(A, O, C) → θ

AI Drawing Prompt Reference

Draw a circle with its center intersecting the x and y axes. From a point on the circle, draw a tangent line and connect the center to this point. Take a point on the tangent line, connect it to the center, and let it intersect the circle at another point. Draw the circular arc from the center to this intersection point, and the line segment connecting the intersection point to the point on the circle. Label the angles formed by the center, the point on the circle, and the tangent point, and show the relationship between the tangent and the arc to demonstrate the concept of limits under small angles.
The prompt above was compiled from the original drawing commands and is for reference only.