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Tangent Graph Unit Circle Trace

Tangent Graph Unit Circle Trace
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2015-02-08 17:03
CircleFunctionTrigonometryCoordinate GeometryDerivative
In collections The Unit Circle and Trigonometric Graphs
This example demonstrates how the trace of a point on the unit circle generates the tangent function graph. Core math concepts include the unit circle, trigonometric functions, derivatives, and analytical geometry. Construction highlights involve commands like Circle, Intersect, Rotate, Angle, Segment, and Line from GeoGebra, as per the summary. Suitable for high school and above students to understand the relationship between trigonometric graphs and the unit circle.

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(O, A) → b
  6. Line(O, A) → a
  7. Intersect(a, d) → C
  8. Segment(B, C) → e
  9. Segment(E, D) → f
  10. Segment(C, D) → g

AI Drawing Prompt Reference

Draw a unit circle and mark the intersection point with the y-axis. Rotate this point around the origin by angle θ to get another point on the circle. Connect the origin to this rotated point. Draw a line parallel to this segment that intersects the y-axis at another point. Connect this intersection point to the rotated point. Finally, connect the rotated point to the y-axis intersection point to show how the trace of a point on the unit circle generates the tangent function graph.
The prompt above was compiled from the original drawing commands and is for reference only.