Exact Trigonometric Values on Unit Circle (Radians)
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This GeoGebra example demonstrates the exact values of trigonometric functions at special angles (0, π/6, π/4, π/3, π/2) on the unit circle using radian measure. Core mathematical concepts include: the unit circle definition, radian system, and exact values of sine, cosine, and tangent for common special angles (30°, 45°, 60°). Construction details: using Intersect to find circle-axis intersections, Point for points on circle, Circle for unit circle, Angle for angle marking, Vector for radius vectors, Polygon for auxiliary polygons, and Distance for length calculations. Suitable for high school trigonometry units, demonstrating relationships between special angle trig values, verifying memory techniques, and analyzing unit circle symmetry.
GeoGebra Commands & Parameters
Intersect(xAxis, yAxis) → OPoint(xAxis) → ECircle(O, E) → c_1Point(c_1) → XSegment(O, X) → aDistance(X, A_1) → bAngle(E, O, X) → αSegment(A_1, (x(A_1), 0)) → fSegment(A_2, (x(A_2), 0)) → gSegment(B_2, B_1) → hSegment(C_2, C_1) → iVector(O, X) → uVector(X, (x(X), 0)) → vVector(X, (0, y(X))) → wPoint(u) → ASegment(A, C_2) → eSegment(A, B_2) → jSegment(A, A_2) → kSegment(A, A_3) → lSegment(A, B_3) → mSegment(A, C_3) → nSegment(A, C_4) → pSegment(A, B_4) → qSegment(A, A_4) → rSegment(A, A_1) → s_1Segment(A, B_1) → tSegment(A, C_1) → a_1Polygon(X, (x(X), 0), A) → poly1, a_2, B, b_1Polygon((abs(x(X)), abs(y(X))), A, (abs(x(X)), 0)) → poly2, d_1, e_1, a_3