Unit Circle Half Angle Diagram
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This example demonstrates the geometric representation of half-angle formulas in the unit circle, dynamically showing the relationship between half-angle trigonometric values and the original angle. Core mathematical concepts include the unit circle, trigonometric functions, half-angle formulas, and complex number representations. Construction highlights involve GeoGebra commands/objects like Intersect, Circle, Point, Vector, Segment, Ray, and Angle. Suitable for high school mathematics education to understand the geometric meaning of trigonometric functions and the application of half-angle formulas.
GeoGebra Commands & Parameters
Intersect(xAxis, yAxis) → OCircle(O, 1) → dPoint(d) → PVector(O, P) → uSegment(Q, P) → eIntersect(d, xAxis, 1) → ASegment(A, P) → aIntersect(a, yAxis) → BRay(A, P) → bIntersect(d, xAxis, 2) → CAngle(C, O, P) → θAngle(C, A, P) → α