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Unit Circle and Sine/Cosine Graphs

Unit Circle and Sine/Cosine Graphs
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2017-01-27 09:10
CircleFunctionTrigonometry
This example visually demonstrates the graphs of sine and cosine functions using the unit circle, helping to understand their definitions. It utilizes commands such as Circle, Point, CircleArc, OrthogonalLine, Intersect, Segment, Polygon, and more to construct the diagram. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Circle(A, B) → c
  2. Point(c) → C
  3. CircleArc(A, B, C) → d
  4. OrthogonalLine(C, xAxis) → a
  5. OrthogonalLine(C, yAxis) → b
  6. Intersect(b, yAxis) → D
  7. Segment(C, D) → e
  8. Intersect(a, xAxis) → E
  9. Segment(C, E) → f
  10. OrthogonalLine(Y, xAxis) → g
  11. Intersect(g, xAxis) → F
  12. Segment(Y, F) → h
  13. Segment(X, F) → i
  14. Segment(A, F) → n
  15. Polygon(G, G2, G3) → poly1, g3, g_1, g2
  16. Angle(G2, G, G3) → α

AI Drawing Prompt Reference

Draw a unit circle centered at the origin. Place a point on the circle, then draw perpendicular lines from this point to the x-axis and y-axis, marking the intersection points. Connect the point to these intersections with line segments. To the right of the circle, plot the sine and cosine graphs, using projections from the circle point to the axes to show function values. On the x-axis, select a point, draw a vertical line from it to intersect the graph, and connect relevant points to form a triangle, labeling its angle. The diagram illustrates the relationship between trigonometric functions and the unit circle.
The prompt above was compiled from the original drawing commands and is for reference only.