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Unit Circle and Graphs of Sine and Cosine

Unit Circle and Graphs of Sine and Cosine
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2013-08-24 06:16
CircleFunctionTrigonometryCoordinate GeometryGeometric Construction
In collections Precal
This example demonstrates the relationship between the unit circle and the graphs of sine and cosine functions. It involves core math concepts like the unit circle, trigonometric functions, and coordinate geometry. Construction uses commands such as Point, Circle, Segment, Angle, OrthogonalLine, Intersect, Polygon in GeoGebra. Suitable for high school mathematics teaching and function graph learning.

GeoGebra Commands & Parameters

  1. Point(yAxis) → A
  2. Circle(A, 1) → c
  3. Segment(A, B) → a
  4. Point(xAxis) → D
  5. Angle(D, A, B) → θ_1
  6. Angle(D, A, F) → α
  7. Segment(A, F) → b
  8. OrthogonalLine(B, xAxis) → d
  9. Intersect(xAxis, d) → G
  10. Point(a) → H
  11. Polygon(B, G, H) → poly1, h, b_1, g_1
  12. Polygon(G, F, H) → poly2, h_1, g_2, f_1

AI Drawing Prompt Reference

Draw a unit circle and mark points related to the sine and cosine function graphs. From the center, draw perpendicular lines to the x-axis and y-axis, marking intersections as D and A. Choose an arbitrary point B on the circle, connect AB and extend it to intersect the x-axis at F. Draw a line perpendicular to the x-axis from B, intersecting the x-axis at G. Extend AG to intersect the x-axis at H. Form two quadrilaterals by connecting B, G, H and G, F, H using the polygon tool, showing the relationship between the unit circle and sine/cosine function graphs.
The prompt above was compiled from the original drawing commands and is for reference only.