Trigonometric Ratios on the Unit Circle by David Murrells
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This example demonstrates the geometric meaning of trigonometric ratios on the unit circle. Using rotation and intersection commands, it shows the sine, cosine, and tangent values. Suitable for high school math education, it helps students understand the relationship between trigonometric functions and the unit circle.
GeoGebra Commands & Parameters
Intersect(xAxis, yAxis) → ACircle(A, 1) → cIntersect(c, xAxis) → B, CRotate(C, 15°, A) → C'Angle(C, A, C') → αRotate(C, 30°, A) → C'_1Angle(C, A, C'_1) → βRotate(C, 45°, A) → C'_2Angle(C, A, C'_2) → γRotate(C, 60°, A) → C'_3Angle(C, A, C'_3) → δRotate(C, 75°, A) → C'_4Angle(C, A, C'_4) → εRotate(C, 90°, A) → C'_5Angle(C, A, C'_5) → ζRotate(C, 105°, A) → C'_6Angle(C, A, C'_6) → ηRotate(C, 120°, A) → C'_7Angle(C, A, C'_7) → θRotate(C, 135°, A) → C'_8Angle(C, A, C'_8) → ιRotate(C, 150°, A) → C'_9Angle(C, A, C'_9) → κRotate(C, 165°, A) → C'_{10}Angle(C, A, C'_{10}) → λRotate(C, 180°, A) → C'_{11}Angle(C, A, C'_{11}) → μRotate(C, 195°, A) → C'_{12}Angle(C, A, C'_{12}) → νRotate(C, 210°, A) → C'_{13}Angle(C, A, C'_{13}) → ξRotate(C, 225°, A) → C'_{14}Angle(C, A, C'_{14}) → οRotate(C, 240°, A) → C'_{15}Angle(C, A, C'_{15}) → ρRotate(C, 255°, A) → C'_{16}Angle(C, A, C'_{16}) → σRotate(C, 270°, A) → C'_{17}Angle(C, A, C'_{17}) → τRotate(C, 285°, A) → C'_{18}Angle(C, A, C'_{18}) → υRotate(C, 300°, A) → C'_{19}Angle(C, A, C'_{19}) → ϕRotate(C, 315°, A) → C'_{20}Angle(C, A, C'_{20}) → χRotate(C, 330°, A) → C'_{21}Angle(C, A, C'_{21}) → ψRotate(C, 345°, A) → C'_{22}Angle(C, A, C'_{22}) → ωPoint(c) → DSegment(A, D) → fLine(D, yAxis) → gIntersect(xAxis, g) → ESegment(D, E) → hSegment(E, A) → iAngle(C, A, D) → α_1Ray(A, D) → jLine(C, yAxis) → kIntersect(j, k) → FSegment(F, C) → lLine(B, yAxis) → mIntersect(j, m) → GSegment(G, B) → n