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Unit Circle and Trigonometric Functions by Paul Leverett

Unit Circle and Trigonometric Functions by Paul Leverett
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2015-01-18 20:10
CircleTrigonometryCoordinate GeometryGeometric Construction
This example demonstrates the geometric interpretation of sine, cosine, tangent, and cotangent functions using the unit circle. It involves core math concepts like the unit circle, trigonometric definitions, and the relationship between angles and coordinates. Construction highlights include using GeoGebra commands such as Intersect, Circle, Point, Segment, OrthogonalLine, and Angle. Suitable for high school students learning trigonometric functions and introductory calculus education.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Circle(A, 1) → c
  3. Point(c) → B
  4. Segment(B, A) → Radius
  5. OrthogonalLine(B, yAxis) → d
  6. OrthogonalLine(B, xAxis) → b
  7. Intersect(b, xAxis) → D
  8. Segment(B, D) → sine
  9. Segment(A, D) → cosine
  10. OrthogonalLine(B, Radius) → a
  11. Intersect(a, xAxis) → C
  12. Intersect(a, yAxis) → E
  13. Segment(B, C) → tangent
  14. Segment(B, E) → cotangent
  15. Segment(D, C) → e
  16. Intersect(c, xAxis, 2) → F
  17. Angle(F, A, B) → α

AI Drawing Prompt Reference

Draw a unit circle and select a point B on it. Draw perpendicular lines from B to the x-axis and y-axis, intersecting at points D and E respectively. Connect B to D and E to form the sine and cosine lines. Then, draw a tangent line from B to the circle, intersecting the x-axis at point C. Connect B to C to form the tangent line, and B to E to form the cotangent line. Finally, use the other intersection point F of the circle with the x-axis to measure the angle ∠FAB.
The prompt above was compiled from the original drawing commands and is for reference only.