Functions, Trigonometry & Geometry

The language of models, shapes and oscillations. Functions and their properties, coordinate geometry from lines to conics and polar curves, and trigonometry from the unit circle to sinusoids — the pre-calculus toolkit for modelling engineering quantities.

• Functions — Functions describe how one quantity depends on another. Learn notation, domain, codomain and range, independent and dependent variables, piecewise, composite and inverse functions, even/odd and periodic functions, monotonicity and boundedness, and the families of algebraic, trigonometric, exponential and logarithmic functions used to model temperature(t), position(t), voltage(t) and pressure(x).
• Coordinate Geometry — Coordinate geometry connects algebra and shapes. Learn Cartesian coordinates, distance and midpoint, slope and straight lines (intercepts, parallel and perpendicular), circles, parabolas, ellipses and hyperbolas (conic sections), parametric curves and polar coordinates — used in CAD, surveying, robotics and optics.
• Trigonometry — Trigonometry links angles and lengths and describes all oscillations. Learn degrees and radians, the unit circle, sine, cosine, tangent and reciprocal functions, inverse trig functions, key identities (Pythagorean, compound, double and half angle, product-to-sum), solving trig equations, the sine and cosine rules, and the amplitude–phase form used in AC circuits and vibrations.