Precalculus and trigonometry together, in course order.
The algebra and equation-solving topics precalculus assumes, gathered up front as a single prerequisite review. Foundational developmental-algebra content lives in Algebra 1 & 2 by Topic; this chapter is the precalc-level refresher.
Graphs, functions, lines, transformations, and function operations — the graphical and functional foundation of precalculus.
Quadratic functions, division and zeros of polynomials, the Fundamental Theorem of Algebra, graphing polynomials, rational functions and asymptotes, and variation.
Inverse functions, exponential functions and equations, logarithms and their properties, the change-of-base theorem, and exponential growth and decay.
The foundational concepts of trigonometry: angles and their measures, angle relationships and similar triangles, the definitions of the six trigonometric functions, quadrantal angles, and the basic (reciprocal, quotient, and Pythagorean) identities.
Trigonometric functions defined through right triangles: acute and non-acute angles, reference angles, approximating function values, significant digits, and applications involving angles of elevation and depression, bearing, distance, and height.
Radian measure and the circular-function view of trigonometry: converting between degrees and radians, arc length and the area of a sector, the unit circle and the values of the circular functions, and linear and angular speed.
Graphing the six trigonometric functions: amplitude, period, and phase shifts of sine and cosine; translations; and the graphs of tangent, cotangent, secant, and cosecant.
Working with trigonometric identities: the fundamental identities, verifying identities, the sum and difference identities, and the double-angle, product-to-sum, and half-angle identities.
The inverse trigonometric functions and their graphs, and solving trigonometric equations by linear and quadratic methods, with multiple and half angles, and with inverse trigonometric functions.
Solving oblique triangles with the Law of Sines (including the ambiguous case) and the Law of Cosines (with Heron’s formula for area), and an introduction to vectors: geometric and algebraic representations, applications, and the dot product.
The trigonometric (polar) form of complex numbers: a review of imaginary numbers, polar form, the product and quotient theorems, De Moivre’s Theorem for powers and roots, and polar coordinate systems and graphing.
Linear and nonlinear systems, Gauss-Jordan elimination, determinants, matrix operations, and inverse matrices.
Parabolas, ellipses, and hyperbolas as conic sections; equations, eccentricity, and the general second-degree equation.
Sequences and series, arithmetic and geometric sequences and series, and the Binomial Theorem.