The Secant and the Unit Circle

This GeoGebra applet provides an interactive demonstration of the relationship between sine, cosine, and secant functions as the central angle varies on the unit circle. It visually illustrates how these trigonometric functions are derived from the circle's geometry, showing their values changing dynamically with the angle. Key mathematical concepts include trigonometric functions, unit circle properties, angle measurement, and the secant function specifically. The construction is achieved using GeoGebra commands such as Intersect for finding points, Point for defining locations, Circle for drawing the unit circle, Segment for creating lines, Angle for representing the central angle, and Line for additional elements. Objects involved include O (the origin), B, g, A, D, a, P, C, c, θ (the variable angle), h, l, d, e, F_1, E, b, F_2, cosine, secant01, secant02, and sine, which together form the visual representation. This example is ideal for educational purposes, particularly in high school trigonometry courses or introductory college mathematics, to enhance understanding of trigonometric identities and graphs.