Sine and Cosine Curves from the Unit Circle

This example demonstrates how the sine and cosine curves can be generated by rotating a point on the unit circle and tracking its coordinates over the angle. It highlights the geometric meaning of trigonometric functions: points on the unit circle parameterize (cos θ, sin θ), producing continuous, periodic graphs. The construction uses a circle with its center, determines the moving point using intersections with angle rays/segments, and applies rotation to advance the angle. Orthogonal/vertical projections are then used to read the x- and y-components corresponding to cos θ and sin θ, which are plotted as the two curves. In the provided construction, key GeoGebra commands and objects include Point (e.g., A, B, C, P), Circle (unit circle), Intersect (computing intersection points), Rotate (rotating around the center), Angle (measuring/constructing θ), Segment (connecting elements), OrthogonalLine (for perpendicular coordinate extraction), and Ray (defining the direction of the angle). Suitable for secondary school through early university use, especially for introducing trig functions via coordinate geometry, visualizing continuity and periodicity, and supporting graphing-based learning.