Unit Circle with Tangents

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2020-03-16 08:52

This example demonstrates how the cosine and sine values of any angle on the unit circle can be represented through the intersection points of tangents with the coordinate axes. Core mathematical concepts include the unit circle, trigonometric functions (sine, cosine), tangents, coordinate geometry, and angles. The construction uses GeoGebra commands such as Intersect, Point, Circle, Segment, and Tangent, as summarized. It is suitable for high school students learning trigonometric functions and analytical geometry, or for mathematical teaching demonstrations.

GeoGebra Commands & Parameters

Intersect(xAxis, yAxis) → A
Point(yAxis) → B
Circle(A, B) → c
Point(c) → C
Segment(A, C) → f
Point(c) → D
Point(c) → E
Point(c) → F
Segment(A, F) → i
Tangent((0.4479550892575661, 0.8940560597682038), c) → g,
Intersect(c, g, 1) → G
Intersect(g, xAxis) → H
Segment(G, H) → h
Tangent((-0.7332872708789501, 0.6799189498513049), c) → j,
Intersect(c, j, 1) → I
Intersect(j, xAxis) → J
Segment(I, J) → k
Point(xAxis) → K
Segment(G, K) → l
Point(xAxis) → L
Segment(I, L) → m
Segment(L, A) → n
Segment(A, K) → p