The Fast Fourier Transform (FFT), developed in 1965 by James Cooley and John Tukey, uses sine and cosine waves to break any signal into its basic frequencies. By projecting time-based data onto these trigonometric waves, FFT reveals the strength and phase of each frequency, like finding the musical notes hidden in a complex sound. This breakthrough in signal processing revolutionized everything from audio compression to medical imaging, all rooted in the power of trigonometry.