A free OpenStax college-level Algebra and Trigonometry textbook covering algebra prerequisites (real numbers, exponents, radicals, polynomials, rational expressions), equations and inequalities, functions and their graphs, linear/polynomial/rational/exponential/logarithmic functions, the trigonometric functions, identities and equations, further trigonometry applications (incl. polar/parametric/vectors), systems and matrices, analytic geometry (conics), and sequences/probability/counting. AlgTrig binding (no calculus preview chapter).
Foundational algebra review: real-number system, exponents and scientific notation, radicals and rational exponents, polynomials, factoring, and rational expressions.
Coordinate systems and graphing; solving linear, quadratic, and other types of equations; complex numbers; linear and absolute-value inequalities.
Foundations of functions: notation, domain/range, rates of change, composition, transformations, absolute-value functions, and inverses.
Linear functions and their graphs, modeling with linear functions, and fitting linear regression models to data.
Quadratic, power, polynomial, and rational functions; division of polynomials; zeros; inverses and radical functions; modeling with variation. Complex numbers were covered in Ch 2.
Exponential and logarithmic functions and their graphs, properties of logarithms, equations, models, and curve-fitting.
Angles, right-triangle trigonometry, the unit-circle definition of sine and cosine, and the other trigonometric functions. Note that AlgTrig orders right-triangle trig before the unit circle, while Precalc 2e places the unit circle first.
Graphs of the trigonometric functions and inverse trigonometric functions.
Verifying identities, sum/difference, double-angle/half-angle/reduction formulas, product-to-sum/sum-to-product, and solving equations.
Non-right triangles (Laws of Sines and Cosines), polar coordinates and graphs, polar form of complex numbers, and vectors.
Linear and nonlinear systems of equations and inequalities; matrices; solving with Gaussian elimination, inverses, and Cramer's Rule.
Conic sections in standard form (ellipse, hyperbola, parabola).
Arithmetic and geometric sequences and series, summation notation, and the binomial theorem.