MathPlotAI Logo MathPlotAI

Interactive Unit Circle by cfisher

Interactive Unit Circle by cfisher
Loading the math board and drawing, please wait…
2012-02-20 23:05
CircleVectorTrigonometryCoordinate GeometryGeometric Construction
This example demonstrates the geometric properties and trigonometric relationships of the unit circle interactively. It involves core math concepts like the definition of the unit circle, trigonometric functions (sin, cos, tan), angles, and vectors. The construction uses GeoGebra commands such as Circle, Intersect, Point, Segment, and Angle. Suitable for high school mathematics teaching to understand trigonometric graphs, vector operations, and geometric constructions.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Circle(A, 1) → c
  3. Mirror(B, yAxis) → B'
  4. Mirror(B, xAxis) → B'_1
  5. Mirror(B', xAxis) → B''
  6. Mirror(C, yAxis) → C'
  7. Mirror(C', xAxis) → C''
  8. Mirror(C'', yAxis) → C'''
  9. Mirror(D, yAxis) → D'
  10. Mirror(D', xAxis) → D''
  11. Mirror(D'', yAxis) → D'''
  12. Point(c) → I
  13. Segment(I, A) → g
  14. Angle(E, A, I) → α

AI Drawing Prompt Reference

Draw a unit circle with its center at the origin and mark the intersection point of the coordinate axes. Draw a radius from the origin to the circle, then symmetrically mark multiple points on the circle based on this radius. Connect the origin to these points on the circle and label the angle between the radius and the x-axis to demonstrate the geometric properties and trigonometric relationships of the unit circle.
The prompt above was compiled from the original drawing commands and is for reference only.