Addition of Two Sine Functions

This GeoGebra example dynamically demonstrates the superposition of two sine functions, showing how their sum produces a composite waveform with periodic characteristics. The core mathematical concepts include amplitude, frequency, phase, and the linear superposition principle of trigonometric functions, along with function graph transformations and periodicity analysis. Construction highlights: using the Segment command to create auxiliary line segments, defining two sine functions f1 and f2, controlling their parameters via points R1, R2 and objects G1C, G2C, and generating the composite function g = f1 + f2. Additional geometric elements such as tangent lines and orthocenter are included for deeper exploration. This is suitable for high school or early college students learning trigonometry and wave superposition, and serves as an intuitive introduction to Fourier series concepts.