Geometric Construction of Sine and Cosine Curves

This example demonstrates sine and cosine curves by using a rotating point on a circle and projecting it onto reference lines. It highlights the geometric meaning of trigonometric functions: how a rotation angle determines the y- and x-projections, producing sinusoidal wave shapes and their phase relationship. Key concepts include trigonometry (sine and cosine), circular motion/parameterization, angle-to-function correspondence, and periodic behavior as the rotation changes. Construction outline: Circle and Point set up the reference circle and key points; Rotate drives the moving point around the circle; OrthogonalLine creates perpendicular projections from the rotating point; Intersect locates key intersection points; Line and Segment connect and define the relevant geometric pieces; Angle labels the rotation angle (e.g., α, β) to relate phase to the curves; CircleArc and text objects (text1/text2) visualize arcs and annotations. Suitable for secondary to early university education, especially for building intuitive understanding of trig functions and graphing sinusoidal functions.