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Changes in Latitude

Changes in Latitude
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2016-04-15 00:40
CircleTrigonometryCoordinate GeometryGeometric Construction
This example demonstrates how to calculate the arc length at a given latitude and longitude angle. Key mathematical concepts include trigonometry, arc length, and coordinate geometry. Construction involves Geogebra commands like Circle, Intersect, and Rotate. Suitable for high school students or college freshmen learning trigonometry and geometric constructions.

GeoGebra Commands & Parameters

  1. Circle(Z, 3960) → c
  2. Intersect(c, xAxis, 2) → Equator
  3. Rotate(Equator, LatitudeOrig, Z) → Equator'
  4. Segment(Z, Equator) → a
  5. Line(Equator', a) → d
  6. Intersect(d, yAxis) → A
  7. Segment(A, Equator') → NewRadius
  8. Angle(Equator, Z, Equator') → α
  9. Segment(Z, Equator') → b
  10. Sphere(Z, 3960) → e
  11. OrthogonalLine(P, xOyPlane) → f
  12. Intersect(f, e) → B, C
  13. Circle(zAxis, C) → g
  14. Center(g) → D
  15. Segment(D, C) → h
  16. Segment(Z, D) → i
  17. Segment(Z, P) → j
  18. Angle(C, Z, P) → LAT
  19. Segment(Z, C) → m
  20. Segment(Z, Equator) → n
  21. Circle(Z, NewRadius) → p
  22. Intersect(p, n, 1) → E
  23. Rotate(P, LongitudeAngle°, Z) → P'
  24. Segment(Z, E) → q
  25. Segment(Z, P') → radius
  26. Angle(E, Z, P', xOyPlane) → Longitude
  27. Distance(P', P) → distanceP'P
  28. CircleArc(Z, P, P', xOyPlane) → t
  29. Textfield(LatitudeOrig) → InputBox1
  30. Textfield(s) → InputBox2
  31. Textfield(LongitudeAngle) → InputBox3
  32. Rotate(Equator, LongitudeAngle°, Z) → Equator'_1
  33. Segment(Z, Equator'_1) → a_1
  34. Segment(Z, Equator) → b_1
  35. CircleArc(Z, Equator, Equator'_1) → c_1
  36. Angle(D, C, Z) → β

AI Drawing Prompt Reference

Draw a globe with the equator and a given latitude line, demonstrating how to calculate the arc length of the latitude line through geometric constructions. Start by drawing the Earth and equator, then rotate the equator to get the target latitude line. Calculate and draw the new radius, and finally determine and label the longitude angle and arc length using spherical geometry to show the calculation process.
The prompt above was compiled from the original drawing commands and is for reference only.