This Algebra and Trigonometry course offers a comprehensive journey through essential mathematical concepts, structured into thirteen chapters:
- Prerequisites: Lays the foundation with real numbers, exponents, scientific notation, radicals, polynomials, and rational expressions.
- Equations and Inequalities: Explores the rectangular coordinate system, linear equations, complex numbers, quadratic and other types of equations, and inequalities.
- Functions: Introduces function notation, domain and range, rates of change, composition, transformations, absolute value, and inverse functions.
- Linear Functions: Focuses on linear functions, their modeling, and fitting linear models to data.
- Polynomial and Rational Functions: Covers quadratic functions, power and polynomial functions, graphs, dividing polynomials, zeros of polynomial functions, rational functions, inverses, radical functions, and modeling using variation.
- Exponential and Logarithmic Functions: Discusses exponential and logarithmic functions, their properties, graphs, equations, models, and data fitting.
- The Unit Circle: Sine and Cosine Functions: Introduces angles, right triangle trigonometry, the unit circle, and other trigonometric functions.
- Periodic Functions: Explores the graphs of sine, cosine, and other trigonometric functions, including inverse trigonometric functions.
- Trigonometric Identities and Equations: Focuses on verifying trigonometric identities, sum and difference identities, double-angle, half-angle, and reduction formulas, and solving trigonometric equations.
- Further Applications of Trigonometry: Covers non-right triangles (Law of Sines and Cosines), polar coordinates, polar graphs, polar form of complex numbers, parametric equations, vectors.
- Systems of Equations and Inequalities: Addresses systems of linear equations in two and three variables, nonlinear systems, partial fractions, matrices, Gaussian elimination, inverses, and Cramer's Rule.
- Analytic Geometry: Delves into the ellipse, hyperbola, parabola, rotation of axes, and conic sections in polar coordinates.
- Sequences, Probability, and Counting Theory: Concludes with sequences and their notations, arithmetic and geometric sequences, series, counting principles, the Binomial Theorem, and probability.
Each chapter is designed to build upon the previous, ensuring a cohesive and comprehensive understanding of algebra and trigonometry.
