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Sine Graph Unit Circle Trace

Sine Graph Unit Circle Trace
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2015-02-08 16:39
CircleTrigonometryGeometric Construction
In collections The Unit Circle and Trigonometric Graphs
This example demonstrates the trajectory of the sine function on the unit circle. Key mathematical concepts include trigonometry, the unit circle, and rotation. Construction involves GeoGebra commands such as Circle, Intersect, Rotate, and Angle. Suitable for high school students learning trigonometric functions and geometric constructions.

GeoGebra Commands & Parameters

  1. Circle(O, 1) → c
  2. Intersect(c, yAxis, 1) → B
  3. Rotate(B, θ, O) → A
  4. Angle(B, O, A) → α
  5. Segment(C, A) → a
  6. Segment(O, A) → b
  7. Segment(E, D) → d
  8. Segment(A, D) → e

AI Drawing Prompt Reference

Draw a unit circle centered at the origin with a radius of 1. Then, find the intersection of the y-axis and the circle to get point B. Rotate point B around the origin O by θ degrees to get point A. Measure the angle ∠BOA to get α. Draw line segment a between C and A, line segment b between O and A, line segment d between E and D, and line segment e between A and D.
The prompt above was compiled from the original drawing commands and is for reference only.