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Trigonometric Function Trajectory on Unit Circle

Trigonometric Function Trajectory on Unit Circle
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2015-02-15 18:07
CircleTrigonometryGeometric Construction
In collections The Unit Circle and Trigonometric Graphs
This example demonstrates the trajectory of trigonometric functions on the unit circle. Key mathematical concepts include trigonometric functions, unit circle, and angles. Using commands like rotation, intersection, and line, it shows how sine and cosine values change with angle variations. Suitable for high school math education and students learning trigonometry.

GeoGebra Commands & Parameters

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

AI Drawing Prompt Reference

Draw a unit circle centered at the origin. Mark the intersection of the circle with the positive y-axis. Rotate this point around the center by an arbitrary angle to get a new point on the circle. Connect the center to this new point with a radius segment, and extend it into a line. This line intersects a horizontal reference line at a point. Draw a segment from the y-axis intersection to this intersection point, another segment from the new point to a fixed point on the y-axis, and finally a segment from the center to that fixed point. The figure illustrates how sine and cosine values change with the angle.
The prompt above was compiled from the original drawing commands and is for reference only.