Video Note-Taking Guide with Integrated Review Worksheets for Precalculus A Unit Circle Approach

Precalculus: A Unit Circle Approach gives you the strength of solid mathematics in an engaging, friendly way. It draws from the authors' extensive classroom experience to connect conceptual understanding while maintaining the level of mathematics required. In the 4th Edition new resources lift you to reach your full potential, including Key Ideas for the next section, objective video and note-taking guides, and much more. Nationally recognized instructors Jessica Bernards and Wendy Fresh join the author team to add fresh perspective to this revision.

About our authors

J.S. Ratti (1935 - 2018) taught mathematics at all levels for over 35 years, most recently as a full professor and past chair of mathematics at the University of South Florida. Professor Ratti was the author of numerous research papers in analysis, graph theory and probability. He received several awards, including a USF Research Council Grant, USF Teaching Incentive Program (TIP) Award, USF Outstanding Undergraduate Teaching Award, and Academy of Applied Sciences grants; he was the coauthor of a successful finite mathematics textbook.

Marcus McWaters is currently an Associate Professor at the University of South Florida (USF). He is a former Chair of the Department of Mathematics and Statistics at USF. Since receiving his PhD in mathematics from the University of Florida, he has taught all levels of undergraduate and graduate courses, with class sizes ranging from 3 to 250. As Chair, he successfully structured a course delivery system for lower-level courses that improved the low retention rate in those courses at USF. He is also a founding member of the USF Center for Digital and Computational Video. When not involved with mathematics or administrative activity, he enjoys traveling with his wife and two daughters, theater, waterskiing and racquetball.

Leslaw Skrzypek is currently the Chair of the Department of Mathematics and Statistics at the University of South Florida. His research is in the area of Banach Spaces and Approximation Theory. He is the recipient of a Fulbright Award and a NATO Advanced Grant research award, and is a founding director of the USF Center for Complex Data Systems. Throughout his career, Professor Skrzypek has enjoyed teaching all levels of courses, from remedial to graduate real analysis. Over the years he also has been involved in training students for the Mathematical Olympiads. He enjoys nature, listening to music and spending time with his family.?

Jessica Bernards has been teaching mathematics since 2005. She began her career at the high-school level and transitioned to teaching at Portland Community College in 2010. She has taught a wide range of mathematics courses from developmental math up to calculus and has created curricula for each level. Bernards is a member of AMATYC's Project ACCCESS Cohort 9, where she developed a math study skills program that is now used across the US. In 2017, she was the honored recipient of the Leila and Simon Peskoff AMATYC Award for her work with Project ACCCESS, and in 2021 received the AMATYC Teaching Excellence Award.

Wendy Fresh has been a full-time instructor at Portland Community College (PCC) since 1997. She has taught a wide range of classes, from developmental math through calculus, both on campus and online. Fresh began her teaching career in 1992 in both rural and urban high schools. Her love of creating curricula to bring classrooms to life has led to work with technologies that complement her many courses. She earned her bachelor's degree in mathematics education from the University of Oregon and her master's degree in the teaching of mathematics from Portland State University.

1. Graphs and Functions

• 1.1 The Coordinate Plane
• 1.2 Graphs of Equations
• 1.3 Lines
• 1.4 Functions
• 1.5 Properties of Functions
• 1.6 A Library of Functions
• 1.7 Transformations of Functions
• 1.8 Combining Functions; Composite Functions
• 1.9 Inverse Functions
• Key Ideas At a Glance
• Review Exercises
• Practice Test

2. Polynomial and Rational Functions

• 2.1 Quadratic Functions
• 2.2 Polynomial Functions
• 2.3 Dividing Polynomials and the Rational Zeros Test
• 2.4 Rational Functions
• 2.5 Polynomial and Rational Inequalities
• 2.6 Zeros of a Polynomial Function
• 2.7 Variation
• Key Ideas At a Glance
• Review Exercises
• Practice Test
• Cumulative Review Exercises Chapters 1-2

3. Exponential and Logarithmic Functions

• 3.1 Exponential Functions
• 3.2 Logarithmic Functions
• 3.3 Rules of Logarithms
• 3.4 Exponential and Logarithmic Equations and Inequalities
• 3.5 Logarithmic Scales; Modeling
• Key Ideas At a Glance
• Review Exercises
• Practice Test
• Cumulative Review Exercises Chapters 1-3

4. Trigonometric Functions

• 4.1 Angles and Their Measure
• 4.2 The Unit Circle; Trigonometric Functions of Real Numbers
• 4.3 Trigonometric Functions of Angles
• 4.4 Graphs of the Sine and Cosine Functions
• 4.5 Graphs of the Other Trigonometric Functions
• 4.6 Inverse Trigonometric Functions
• Key Ideas At a Glance
• Review Exercises
• Practice Test
• Cumulative Review Exercises Chapters 1-4

5. Analytic Trigonometry

• 5.1 Trigonometric Identities
• 5.2 Sum and Difference Formulas
• 5.3 Double-Angle and Half-Angle Formulas
• 5.4 Product-to-Sum and Sum-to-Product Formulas
• 5.5 Trigonometric Equations I
• 5.6 Trigonometric Equations II
• Key Ideas At a Glance
• Review Exercises
• Practice Test
• Cumulative Review Exercises Chapters 1-5

6. Applications of Trigonometric Functions

• 6.1 Right-Triangle Trigonometry
• 6.2 The Law of Sines
• 6.3 The Law of Cosines
• 6.4 Vectors
• 6.5 The Dot Product
• 6.6 Polar Coordinates
• 6.7 Polar Form of Complex Numbers; DeMoivre's Theorem
• Key Ideas At a Glance
• Review Exercises
• Practice Test
• Cumulative Review Exercises Chapters 1-6

7. Systems of Equations and Inequalities

• 7.1 Systems of Equations in Two Variables
• 7.2 Systems of Linear Equations in Three Variables
• 7.3 Systems of Inequalities
• 7.4 Matrices and Systems of Equations
• 7.5 Determinants and Cramer's Rule
• 7.6 Partial-Fraction Decomposition
• 7.7 Matrix Algebra
• 7.8 The Matrix Inverse
• Key Ideas At a Glance
• Review Exercises
• Practice Test
• Cumulative Review Exercises Chapters 1-7

8. Analytic Geometry

• 8.1 Conic Sections: Overview
• 8.2 The Parabola
• 8.3 The Ellipse
• 8.4 The Hyperbola
• 8.5 Rotation of Axes
• 8.6 Polar Equations of Conics
• 8.7 Parametric Equations
• Key Ideas At a Glance
• Review Exercises
• Practice Test
• Cumulative Review Exercises Chapters 1-8

9. Further Topics in Algebra

• 9.1 Sequences and Series
• 9.2 Arithmetic Sequences; Partial Sums
• 9.3 Geometric Sequences and Series
• 9.4 Mathematical Induction
• 9.5 The Binomial Theorem
• 9.6 Counting Principles
• 9.7 Probability
• Key Ideas At a Glance
• Review Exercises
• Practice Test
• Cumulative Review Exercises Chapters 1-9

10. An Introduction to Calculus

• 10.1 Finding Limits Using Tables and Graphs
• 10.2 Finding Limits Algebraically
• 10.3 Infinite Limits and Limits at Infinity
• 10.4 Introduction to Derivatives
• 10.5 Area and the Integral
• Key Ideas At a Glance
• Review Exercises
• Practice Test

A. Review

• A.1 The Real Numbers; Integer Exponents
• A.2 Polynomials
• A.3 Rational Expressions
• A.4 Radicals and Rational Exponents
• A.5 Topics in Geometry
• A.6 Equations
• A.7 Inequalities
• A.8 Complex Numbers

Answers to Selected Exercises

Credits

Index

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