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Trigonometric Functions on the Unit Circle by Michael L. Daly-Jones

Trigonometric Functions on the Unit Circle by Michael L. Daly-Jones
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2017-07-05 22:31
CircleFunctionTrigonometry
This example demonstrates the geometric meaning of trigonometric functions using the unit circle. Key mathematical concepts include trigonometric functions, the unit circle, and angles. By constructing points, intersections, line segments, and angles on the circle, the graphs of sine, cosine, tangent, cotangent, secant, and cosecant functions are shown. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Point(c) → P
  2. Intersect(xAxis, yAxis) → O
  3. Segment(O, P) → f
  4. OrthogonalLine(P, xAxis) → g
  5. OrthogonalLine(P, yAxis) → h
  6. Intersect(g, xAxis) → C
  7. Intersect(h, yAxis) → S
  8. Segment(P, C) → i
  9. Segment(C, O) → j
  10. Segment(P, S) → k
  11. Segment(S, O) → l
  12. Intersect(c, xAxis, 2) → A
  13. Angle(A, O, P) → θ

AI Drawing Prompt Reference

Draw a unit circle and mark a point P on it. Draw a line segment f from the center O to P. Draw a vertical line g through P to the x-axis, intersecting at point C. Draw a vertical line h through P to the y-axis, intersecting at point S. Draw line segments PC, CO, PS, and SO. Take a point A on the x-axis such that the angle between OA and OP is θ.
The prompt above was compiled from the original drawing commands and is for reference only.