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Unit Circle Exploration

Unit Circle Exploration
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2018-12-04 01:54
CircleTrigonometryCoordinate GeometryGeometric Construction
This example demonstrates the relationship between any point on the unit circle, its coordinates, and the angle it forms with the positive x-axis by dragging the red point. Core math concepts include the unit circle, trigonometric functions (sine and cosine), angles, and right triangle side lengths. GeoGebra commands used are Intersect, Point, Circle, Angle, Polygon, and Segment. Suitable for high school students to understand the definition of trigonometric functions and properties of the unit circle, as well as for analytical geometry instruction.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → O
  2. Point(xAxis) → B
  3. Circle(O, B) → c
  4. Point(c) → A
  5. Angle(B, O, A) → α
  6. Polygon(O, C, A) → poly1, adj, opp, hyp
  7. Segment(O, S) → sinα
  8. Segment(O, C) → cosα
  9. Segment(A, O) → a
  10. Angle(A, C, O) → β