Trig Reference Circle with Custom Radius
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Creating Trig Equations: Open Middle Exercises
This example demonstrates a trigonometric reference circle with a customizable radius. It illustrates the geometric meaning of sine and cosine functions and how to construct their graphs using rotation, mirroring, and other commands. Suitable for high school math education and students learning trigonometric functions.
GeoGebra Commands & Parameters
Point(Ray[(0, 0), (1, 0)]) → LCircle((0, 0), L) → cIntersect(xAxis, yAxis) → AIntersect(c, xAxis, 2) → BRotate(L, π / 6, A) → CRotate(L, π / 4, A) → DRotate(L, π / 3, A) → EMirror(C, yAxis) → C'Mirror(D, yAxis) → D'Mirror(E, yAxis) → E'Mirror(E', xAxis) → E''Mirror(D', xAxis) → D''Mirror(C', xAxis) → C''Mirror(C, xAxis) → C'_{1}Mirror(D, xAxis) → D'_{1}Mirror(E, xAxis) → E'_{1}Intersect(c, xAxis, 1) → GIntersect(c, yAxis, 1) → HIf(a ≟ 1, B, a ≟ 6, E', a ≟ 7, D', a ≟ 8, C', a ≟ 9, G, a ≟ 10, C'', a ≟ 2, a ≟ 11, D'', a ≟ 12, E'', a ≟ 13, H, a ≟ 14, E'_{1}, a ≟ 15, D'_{1}, C, a ≟ 16, C'_{1}, a ≟ 3, D, a ≟ 4, E, a ≟ 5, F) → PIntersect(eq1, xAxis) → IPolygon(A, I, P) → t1, p, a_1, iSegment(A, P) → fAngle(P, I, A) → αMidpoint(A, P) → JSegment(A, P) → jSegment(A, I) → kSegment(I, P) → lAngle(I, A, P) → βVector(A, I) → uSurdText(x(I)) → text3SurdText(y(P)) → text4Vector(I, P) → vAngle(B, A, P) → γIf(a ≟ 1, L, a ≟ 6, E', a ≟ 7, D', a ≟ 8, C', a ≟ 9, G, a ≟ 10, C'', a ≟ 2, a ≟ 11, D'', a ≟ 12, E'', a ≟ 13, H, a ≟ 14, E'_{1}, a ≟ 15, D'_{1}, C, a ≟ 16, C'_{1}, a ≟ 3, D, a ≟ 4, E, a ≟ 5, F) → KDilate(K, 2, (0, 0)) → K'
AI Drawing Prompt Reference
Draw a trigonometric reference circle with a customizable radius centered at the origin. Mark points on the circle at angles π/6, π/4, and π/3, and their respective reflections across the y-axis. Then, reflect the π/6 point twice across the x-axis, and connect the origin to these points to form a triangle, labeling the angles and vectors.
The prompt above was compiled from the original drawing commands and is for reference only.