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Graphing Sine and Cosine with Unit Circle

Graphing Sine and Cosine with Unit Circle
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2020-06-12 01:56
CircleFunctionTrigonometryGeometric ConstructionGraphing
This example dynamically demonstrates how the unit circle and corresponding right triangles generate sine and cosine function graphs. It involves core math concepts like the unit circle, trigonometric definitions, right triangle side-angle relationships, and function graph plotting. GeoGebra commands used include Intersect, Circle, Point, Segment, Angle, and If to construct the unit circle, triangle relationships, and function plots. Suitable for high school trigonometry and introductory calculus students learning function graph origins.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Circle(A, 1) → c
  3. Point(c) → B
  4. Segment(A, B) → a
  5. Angle(C, A, B) → α
  6. Segment(D, F) → b
  7. Segment(E, C) → d
  8. If(0 ≤ x ≤ 6.28319, sin(x)) → f
  9. If(0 ≤ x ≤ 6.28319, cos(x)) → g
  10. Segment(A, G) → e
  11. Segment(B, G) → h
  12. Segment(B, H) → i
  13. Segment(J, I) → j
  14. Segment(I, L) → k
  15. Segment(B, G) → p

AI Drawing Prompt Reference

Draw a unit circle with a point marked on it. Construct a right triangle using the point and the circle's radius. Show the sides and angles of the triangle. Plot the sine and cosine function graphs. Project the point on the circle onto the coordinate axes and connect the projections to the corresponding points on the sine and cosine graphs to dynamically demonstrate the relationship between the unit circle, right triangle, and the function graphs.
The prompt above was compiled from the original drawing commands and is for reference only.