Pre-calculus: trigonometry and logarithms

Trigonometry and logarithms — the working subset.

Trigonometry is the language of oscillation: every wave, phasor, and Fourier component is built on $\sin$ and $\cos$. Logarithms compress quantities that span many orders of magnitude — sound pressures from a whisper to a jet engine, frequencies across ten octaves — into a linear axis on which equal ratios become equal distances; the decibel is one such axis.

• 0.1 Trigonometry — the radian, the unit-circle definition of sine and cosine, the Pythagorean identity, the amplitude–period–phase reading of $A\cos(\omega t + \varphi)$, and the angle-sum, double-angle, and product-to-sum identities.
• 0.2 Logarithms and exponentials — exponential and logarithm laws, the natural base $e$, change of base, exponential growth and decay, and the decibel.