Trigonometric Function Values with Triangle and Circle

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2015-01-29 06:45

This example demonstrates the geometric meaning of trigonometric function values using a triangle and a circle. Key mathematical concepts include trigonometric functions (sine, cosine, tangent, etc.) and their representation on the unit circle. Construction highlights include the use of intersection, circle, segment, and tangent commands. Suitable for high school math education and students learning trigonometry.

GeoGebra Commands & Parameters

Intersect(xAxis, yAxis) → A
Point(xAxis) → B
Circle(A, B) → c
Point(c) → C
Segment(A, C) → radius
Tangent(C, c) → b,
Intersect(b, xAxis) → D
Intersect(yAxis, b) → E
Angle(B, A, C) → α
Radius(c) → r
OrthogonalLine(C, xAxis) → j
Intersect(j, xAxis) → F
Segment(A, F) → cosine
Segment(F, C) → sine
Segment(A, E) → cosecant
Segment(C, D) → tangent_1
Segment(C, E) → cotangent_1
Segment(A, D) → secant
Angle(C, F, A) → β
Segment(C, F) → vertical
Line(A, C) → l
Intersect(l, k) → G
Segment(If[x(C) ≥ 0, B, ((-x(B)), 0)], G) → tangent_2
OrthogonalLine(G, yAxis) → n
Intersect(n, yAxis) → H
Segment(H, G) → cotangent_2
Segment(A, G) → i

AI Drawing Prompt Reference

Draw a unit circle with a point on the x-axis and the origin. Connect these two points to form the radius. From the intersection point on the circle, draw a tangent line that intersects the x-axis and y-axis at two points. Represent the cosine with the distance from the origin to the intersection on the tangent, and the sine with the distance from this intersection to the circle. Draw and label the tangent, cotangent, secant, and cosecant lines, and indicate the angle relationships.

The prompt above was compiled from the original drawing commands and is for reference only.