Unit Circle Showing the 6 Trig Functions
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This GeoGebra example visualizes all six trigonometric functions—sine, cosine, tangent, cotangent, secant, and cosecant—on the unit circle, dynamically linking each function's value to the angle as a point moves around the circle. It demonstrates the unit circle definition of trigonometric functions, the ratios of sides in right triangles, and the periodic nature of these functions. The construction uses GeoGebra commands such as Intersect, Circle, Point, Segment, Tangent, OrthogonalLine, Angle, and LaTeX text objects to create a rich diagram with radius, perpendicular segments, tangents, and angle labels. This resource is ideal for high school or introductory college students learning trigonometry, as well as for teachers demonstrating the geometric origins of trigonometric ratios in an interactive classroom setting.
GeoGebra Commands & Parameters
Intersect(xAxis, yAxis) → ACircle(A, B) → fPoint(f) → CSegment(A, C) → gTangent(C, f) → h,Intersect(h, i) → DIntersect(h, j) → ESegment(E, C) → kSegment(C, D) → lSegment(A, D) → mSegment(A, E) → nOrthogonalLine(C, n) → pOrthogonalLine(C, m) → qIntersect(j, p) → FIntersect(i, q) → GSegment(F, C) → rSegment(C, G) → sAngle(B, A, C) → αLaTeX(α, true, true) → text1
AI Drawing Prompt Reference
Visualize all six trigonometric functions on a unit circle, showing how sine, cosine, tangent, cotangent, secant, and cosecant relate to the angle as a point moves around the circle. Start with the intersection of the x and y axes, then draw a unit circle. Plot the sine value as a point on the y-axis, cosine on the x-axis, and represent tangent with a tangent line and perpendicular segments. Include dynamic angle labels, tangents, and perpendiculars, clearly demonstrating the geometric origins and periodic nature of trigonometric functions.
The prompt above was compiled from the original drawing commands and is for reference only.