Algebra & Trigonometry 2e — Deep Notes
Comprehensive notes from Algebra and Trigonometry 2e (OpenStax). Covers prerequisites through advanced trigonometry, analytic geometry, and sequences — from foundational concepts to complex problem-solving. Every chapter, every topic, every key concept.
Part 1 — Foundations
🔢 Ch 1 · Prerequisites
Real numbers, order of operations, exponents, scientific notation, radicals, polynomials, factoring, rational expressions.
⚖️ Ch 2 · Equations and Inequalities
Linear equations, linear inequalities, absolute value, quadratic equations, complex numbers, rational & radical equations.
Part 2 — Functions and Their Graphs
📐 Ch 3 · Functions
Function notation, domain & range, rates of change, composition, transformations, absolute value functions, inverse functions.
📏 Ch 4 · Linear Functions
Linear functions, slope, modeling with linear functions, fitting linear models to data.
Part 3 — Polynomial and Rational Functions
📈 Ch 5 · Polynomial and Rational Functions
Quadratic functions, power functions, graphing polynomials, dividing polynomials, zeros, rational functions, variation.
Part 4 — Exponential and Logarithmic Functions
🚀 Ch 6 · Exponential and Logarithmic Functions
Exponential functions, logarithmic functions, properties of logarithms, exponential & log equations, growth/decay models.
Part 5 — Trigonometric Functions
🔵 Ch 7 · The Unit Circle: Sine and Cosine Functions
Angles, right triangle trigonometry, unit circle, the other trigonometric functions.
🌊 Ch 8 · Periodic Functions
Graphs of sine & cosine, graphs of other trig functions, inverse trigonometric functions.
Part 6 — Trigonometric Identities and Applications
🔗 Ch 9 · Trigonometric Identities and Equations
Verifying identities, sum & difference formulas, double-angle & half-angle, product-to-sum, solving trig equations.
📐 Ch 10 · Further Applications of Trigonometry
Law of Sines, Law of Cosines, polar coordinates, polar graphs, complex numbers in polar form, parametric equations, vectors.
Part 7 — Systems and Matrices
🧮 Ch 11 · Systems of Equations and Inequalities
Systems in 2 & 3 variables, nonlinear systems, partial fractions, matrices, Gaussian elimination, inverses, Cramer's rule.
Part 8 — Analytic Geometry
🔮 Ch 12 · Analytic Geometry
The ellipse, the hyperbola, the parabola, rotation of axes, conic sections in polar coordinates.
Part 9 — Sequences, Probability, and Counting
🎲 Ch 13 · Sequences, Probability, and Counting Theory
Sequences, arithmetic & geometric sequences, series, counting principles, binomial theorem, probability.