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Trigonometric Functions on the Unit Circle by Tony Walsh

Trigonometric Functions on the Unit Circle by Tony Walsh
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2014-06-25 17:50
CircleFunctionTrigonometryGeometric ConstructionSlider Animation
This example demonstrates the relationship between angles and trigonometric values using the unit circle. Key concepts include trigonometric functions, unit circle, and angles. GeoGebra commands used include slider, circle, point, segment, and rotation. Suitable for high school math education to help students understand the basic properties of trigonometric functions.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Circle(A, 1) → c
  3. Point(c) → B
  4. Segment(C, B) → b
  5. Rotate(C, α_1, A) → C'
  6. Angle(C, A, C') → α
  7. Ray(A, C') → a
  8. Intersect(c, a) → D,
  9. Segment(A, D) → e
  10. Segment(E, D) → f
  11. Segment(A, E) → d

AI Drawing Prompt Reference

Draw a unit circle and mark a point on it. Draw a line segment from the origin to the point. Use a slider to control an angle, rotate the line segment around the origin by this angle, and get a new line segment. Find the intersection point of the rotated line segment with the unit circle, and draw line segments from the origin to this point and from this point to another point, demonstrating the relationship between trigonometric functions and angles.
The prompt above was compiled from the original drawing commands and is for reference only.