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Trig Functions of Special Angles on the Unit Circle

Trig Functions of Special Angles on the Unit Circle
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2015-05-29 23:18
CircleFunctionTrigonometry
This example demonstrates the trigonometric functions of special angles on the unit circle. Key mathematical concepts include trigonometric functions, the unit circle, and angles. Using GeoGebra commands such as Intersect, Point, Circle, Rotate, etc., it dynamically shows the rotation of angles and changes in trigonometric values. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Circle(A, B) → c
  4. Rotate(B, θ, A) → B'
  5. Segment(A, B') → b
  6. Angle(B, A, B') → α
  7. SurdText(d) → text2
  8. SurdText(f) → text3
  9. IsInteger(12 / a) → e
  10. GCD(a, 12) → g
  11. Dilate(B', 1.2, A) → B''
  12. OrthogonalLine(B', h) → i
  13. Intersect(h, i) → C
  14. Segment(B', C) → j
  15. Segment(C, A) → k

AI Drawing Prompt Reference

Draw a graph of trigonometric functions of special angles on the unit circle. The circle has its center at the origin and radius 1. Mark points A and B on the circle, with B on the x-axis. Draw a line segment from A to B, and rotate B to get B'. Connect A and B' with a line segment, and label the angle α. Also draw a line segment from B' to another point, and find its intersection with a perpendicular line to get point C. Finally, connect C and A to complete the figure.
The prompt above was compiled from the original drawing commands and is for reference only.