About this app
Algebra and Trigonometry provides a comprehensive exploration of algebraic principles and meets scope and sequence requirements for a typical introductory algebra and trigonometry course. The modular approach and the richness of content ensures that the book meets the needs of a variety of courses. Algebra and Trigonometry offers a wealth of examples with detailed, conceptual explanations, building a strong foundation in the material before asking students to apply what they’ve learned.1. Prerequisites
t1. Introduction to prerequisites
t1.1. Real numbers: algebra essentials
t1.2. Exponents and scientific notation
t1.3. Radicals and rational exponents
t1.4. Polynomials
t1.5. Factoring polynomials
t1.6. Rational expressions
2. Equations and inequalities
t2. Introduction to equations and inequalities
t2.1. The rectangular coordinate systems and graphs
t2.2. Linear equations in one variable
t2.3. Models and applications
t2.4. Complex numbers
t2.5. Quadratic equations
t2.6. Other types of equations
t2.7. Linear inequalities and absolute value inequalities
3. Functions
t3. Introduction to functions
t3.1. Functions and function notation
t3.2. Domain and range
t3.3. Rates of change and behavior of graphs
t3.4. Composition of functions
t3.5. Transformation of functions
t3.6. Absolute value functions
t3.7. Inverse functions
4. Linear functions
t4. Introduction to linear functions
t4.2. Modeling with linear functions
t4.3. Fitting linear models to data
5. Polynomial and rational functions
t5. Introduction to polynomial and rational functions
t5.1. Quadratic functions
t5.2. Power functions and polynomial functions
t5.3. Graphs of polynomial functions
t5.4. Dividing polynomials
t5.5. Zeros of polynomial functions
t5.6. Rational functions
t5.7. Inverses and radical functions
t5.8. Modeling using variation
6. Exponential and logarithmic functions
t6. Introduction to exponential and logarithmic functions
t6.1. Exponential functions
t6.2. Graphs of exponential functions
t6.3. Logarithmic functions
t6.4. Graphs of logarithmic functions
t6.5. Logarithmic properties
t6.6. Exponential and logarithmic equations
t6.7. Exponential and logarithmic models
t6.8. Fitting exponential models to data
7. The unit circle: sine and cosine functions
t7. Introduction to the unit circle: sine and cosine functions
t7.1. Angles
t7.2. Right triangle trigonometry
t7.3. Unit circle
t7.4. The other trigonometric functions
8. Periodic functions
t8. Introduction to periodic functions
t8.1. Graphs of the sine and cosine functions
t8.2. Graphs of the other trigonometric functions
t8.3. Inverse trigonometric functions
9. Trigonometric identities and equations
t9. Introduction to trigonometric identities and equations
t9.1. Solving trigonometric equations with identities
t9.2. Sum and difference identities
t9.3. Double-angle, half-angle, and reduction formulas
t9.4. Sum-to-product and product-to-sum formulas
10. Further applications of trigonometry
t10. Introduction to further applications of trigonometry
t10.1. Non-right triangles: law of sines
t10.2. Non-right triangles: law of cosines
t10.3. Polar coordinates
t10.4. Polar coordinates: graphs
t10.5. Polar form of complex numbers
t10.6. Parametric equations
t10.7. Parametric equations: graphs
t10.8. Vectors
11. Systems of equations and inequalities
t11. Introduction to systems of equations and inequalities
t11.1. Systems of linear equations: two variables
t11.2. Systems of linear equations: three variables
t11.3. Systems of nonlinear equations and inequalities: two variables
t11.4. Partial fractions
t11.5. Matrices and matrix operations
t11.6. Solving systems with gaussian elimination
t11.7. Solving systems with inverses
t11.8. Solving systems with cramer's rule
12. Analytic geometry
t12. Introduction to analytic geometry
t12.1. The ellipse
t12.2. The hyperbola
t12.3. The parabola
t12.4. Rotation of axes
t12.5. Conic sections in polar coordinates
13. Sequences, probability, and counting theory
