Physics didn’t pick sinusoids because it “only knows about sinuses.” Physics picked them because the math forces them on you.

Actual engineers:

  - use sinusoids because LTI systems respond, uh... linearly to them
  - use square waves for digital logic
  - use triangle waves for modulation
  - use wavelets for compression or time/frequency localization
  - use Hilbert transforms (and actually know what "orthonormal" means)
  - use STFT, CWT, FFTs... and know exactly why Fourier works and when it breaks