Unit Circle and Sine/Cosine Functions
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This example dynamically demonstrates the correspondence between a point on the unit circle and the sine/cosine functions in the Cartesian coordinate system, visually showing the definition of trigonometric functions. Core math concepts include the unit circle, trigonometric function definitions, Cartesian coordinates, and sine/cosine functions. Construction highlights involve GeoGebra commands/objects like Circle, Point, CircleArc, OrthogonalLine, Intersect, Segment, Polygon, and Angle. Suitable for high school students learning trigonometric graphs and properties, or for introductory calculus teaching on the geometric origin of function graphs.
GeoGebra Commands & Parameters
Circle(A, B) → cPoint(c) → CCircleArc(A, B, C) → dOrthogonalLine(C, xAxis) → aOrthogonalLine(C, yAxis) → bIntersect(b, yAxis) → DSegment(C, D) → eIntersect(a, xAxis) → ESegment(C, E) → fOrthogonalLine(Y, xAxis) → gIntersect(g, xAxis) → FSegment(Y, F) → hSegment(X, F) → iSegment(A, F) → nPolygon(G, G2, G3) → poly1, g3, g_1, g2Angle(G2, G, G3) → α