Basic Sine, Cosine, and Tangent Introduction

①This example dynamically demonstrates the definitions and geometric meanings of the three basic trigonometric functions—sine, cosine, and tangent—using a unit circle and right triangles, showing how function values change as the angle varies. ②Core mathematical concepts include trigonometric definitions, similar triangles, the unit circle, angle-radian correspondence, and the relationship between side ratios in right triangles and function values. ③Construction highlights: using GeoGebra commands such as Intersect to find circle-line intersections, CircleArc to draw arcs, OrthogonalLine to create perpendiculars for right triangles, Segment to connect key sides, Angle to mark angles, and Line for reference lines; objects include radius, angles α, β, γ, δ, points A–H, and segments a–j, with sliders to adjust angles and observe value changes. ④Suitable for high school or pre-university students learning trigonometry, and useful for classroom demonstrations or self-exploration to build an intuitive bridge from geometry to functions.