Dynamic Relationship Between Unit Circle and Sine/Cosine Curves

This interactive GeoGebra example demonstrates how a point moving on the unit circle generates the sine and cosine function curves. It visualizes the fundamental trigonometric definitions: for any angle, the x-coordinate of the point on the unit circle equals cosine, and the y-coordinate equals sine. The construction uses commands such as Intersect, Segment, Point, and Angle to define the circle, the moving point, and the connecting segments. Slider animation (button1, anim) controls the angle, while text objects display angle measures in degrees and radians, and the corresponding function values. The projection of the point onto the axes is traced to form the sine and cosine graphs, showing their periodic nature and phase shift. This resource is ideal for high school trigonometry or introductory college mathematics, helping students grasp the geometric origin of trigonometric functions and their graphical representation.