Trigonometric Function
Launch this tool in a distraction-free environment optimized for classroom instruction.
About
What is the Trigonometric Function?
The Trigonometric Function explorer is a powerful cross-disciplinary sandbox that seamlessly bridges the gap between visual mathematics, the physics of soundwaves, and musical composition. By manipulating the core equation y = a·sin(b(x-c)) + d, students can simultaneously see the wave shift on a graph and hear the acoustic frequencies change in real-time.
STEM connections
This tool beautifully connects Science, Technology, Engineering, Arts, and Mathematics into one cohesive experience.
Mathematics: Graph Transformations
Graph Sine and Cosine waves dynamically. Observe how a (Amplitude) causes a vertical stretch, while b (Frequency) causes a horizontal compression. Master translations by using c and d to shift the wave across the Cartesian plane, and use the "Auto 1 Period" toggle to perfectly frame a single wave cycle!
Physics: Acoustics & Soundwaves
Experience the science of sound. By turning on the Continuous Drone, students will immediately realize that a higher Amplitude (a taller graph) results in a louder Volume, and a higher Frequency (more compressed waves) results in a higher acoustic Pitch measured in Hertz (Hz).
Arts: Musical Synthesizer
Transform your computer keyboard into a playable digital instrument! Open the Keyboard panel and play melodies. Use the Key Configuration table to literally "tune" individual piano keys by typing in custom mathematical b values, creating your own unique microtonal scales.