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Complete Trig Function Demo on Unit Circle

Complete Trig Function Demo on Unit Circle
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2017-06-19 21:16
CircleTrigonometryCoordinate GeometryGeometric Construction
This example demonstrates the geometric interpretation and calculation of trigonometric values (sine, cosine, tangent, etc.) for any angle on the unit circle. It involves core math concepts like the unit circle, angles, trigonometric functions, coordinate geometry, and limits. The construction uses GeoGebra commands and objects such as Segment, Intersect, OrthogonalLine, and Angle. Suitable for high school and above students for visualizing trigonometric definitions and properties, aiding teaching and learning.

GeoGebra Commands & Parameters

  1. Segment(A, B) → r
  2. Segment(A, C) → g
  3. Segment(C, B) → h
  4. Intersect(c, r, 1) → D
  5. OrthogonalLine(D, r) → f
  6. Intersect(f, xAxis) → E
  7. Segment(D, E) → i
  8. Angle(C, A, B) → α
  9. Intersect(r, g) → I
  10. Intersect(c, xAxis, 2) → J
  11. Segment(I, J) → j
  12. Angle(j, r) → θ
  13. Intersect(r, g) → K
  14. Segment(K, E) → k
  15. Intersect(f, yAxis) → L
  16. Segment(D, L) → l
  17. Segment(K, L) → m

AI Drawing Prompt Reference

Draw a unit circle and an angle θ on it, including sine, cosine, and tangent lines. First, draw a line segment from the center of the circle to the intersection of the terminal side of the angle and the circle. Then, draw a perpendicular line from this intersection to the x-axis to form the sine line. Next, draw a line segment from the center to the intersection of the terminal side of the angle and the tangent line to form the cosine line. Finally, draw a line segment from the intersection of the terminal side of the angle and the tangent line to the intersection of the perpendicular line and the y-axis to form the tangent line.
The prompt above was compiled from the original drawing commands and is for reference only.