Guided Lecture Notes with Integrated Review Worksheets for Trigonometry

Description

Mike Sullivan recently retired as Professor of Mathematics at Chicago State University, having taught there for more than 30 years. He received his PhD in mathematics from Illinois Institute of Technology. He is a native of Chicago’s South Side and currently resides in Oak Lawn, Illinois. Mike has four children; the two oldest have degrees in mathematics and assisted in proofing, checking examples and exercises, and writing solutions manuals for this project. His son, Mike Sullivan, III, co-authored the Sullivan Graphing with Data Analysis series as well as this series. Mike has authored or co-authored more than ten books. He owns a travel agency, and splits his time between a condo in Naples, Florida and a home in Oak Lawn, where Mike enjoys gardening.

Mike Sullivan, III is a professor of mathematics at Joliet Junior College. He holds graduate degrees from DePaul University in both mathematics and economics. Mike is an author or co-author on more than 20 books, including a statistics book and a developmental mathematics series. Mike is the father of three children and an avid golfer who tries to spend as much of his limited free time as possible on the golf course.

Guided Lecture Notes ask students to complete definitions, procedures, and examples based on the content of the Author in Action videos and text. By directing students into essential material, students can focus and retain the most important concepts. These notes help increase the success of your students in any course structure.

0135244749 / 9780135244746 GUIDED LECTURE NOTES FOR TRIGONOMETRY: A UNIT CIRCLE APPROACH, 11/e

1. Graphs and Functions
   • 1.1 The Distance and Midpoint Formulas
   • 1.2 Graphs of Equations in Two Variables; Circles
   • 1.3 Functions and Their Graphs
   • 1.4 Properties of Functions
   • 1.5 Library of Functions; Piecewise-defined Functions
   • 1.6 Graphing Techniques: Transformations
   • 1.7 One-to-One Functions; Inverse Functions
   • Chapter 1 Review, Test, and Projects
2. Trigonometric Functions
   • 2.1 Angles, Arc, Length, and Circular Motion
   • 2.2 Trigonometric Functions: Unit Circle Approach
   • 2.3 Properties of the Trigonometric Functions
   • 2.4 Graphs of the Sine and Cosine Functions
   • 2.5 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions
   • 2.6 Phase Shift; Sinusoidal Curve Fitting
   • Chapter 2 Review, Test, and Projects
3. Analytic Trigonometry
   • 3.1 The Inverse Sine, Cosine, and Tangent Functions
   • 3.2 The Inverse Trigonometric Functions (Continued)
   • 3.3 Trigonometric Equations
   • 3.4 Trigonometric Identities
   • 3.5 Sum and Difference Formulas
   • 3.6 Double-angle and Half-angle Formulas
   • 3.7 Product-to-Sum and Sum-to-Product Formulas
   • Chapter 3 Review, Test, and Projects
4. Applications of Trigonometric Functions
   • 4.1 Right Triangle Trigonometry; Applications
   • 4.2 The Law of Sines
   • 4.3 The Law of Cosines
   • 4.4 Area of a Triangle
   • 4.5 Simple Harmonic Motion; Damped Motion; Combining Waves
   • Chapter 4 Review, Test, and Projects
5. Polar Coordinates; Vectors
   • 5.1 Polar Coordinates
   • 5.2 Polar Equations and Graphs
   • 5.3 The Complex Plane; De Moivre’s Theorem
   • 5.4 Vectors
   • 5.5 The Dot Product
   • 5.6 Vectors in Space
   • 5.7 The Cross Produc
   • Chapter 5 Review, Test, and Projects
6. Analytic Geometry
   • 6.1 Conics
   • 6.2 The Parabola
   • 6.3 The Ellipse
   • 6.4 The Hyperbola
   • 6.5 Rotation of Axes; General Form of a Conic
   • 6.6 Polar Equations of Conics
   • 6.7 Plane Curves and Parametric Equations
   • Chapter 6 Review, Test, and Projects
7. Exponential and Logarithmic Functions
   • 7.1 Exponential Functions
   • 7.2 Logarithmic Functions
   • 7.3 Properties of Logarithms
   • 7.4 Logarithmic and Exponential Equations
   • 7.5 Financial Models
   • 7.6 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth and Decay
   • 7.7 Building Exponential, Logarithmic, and Logistic Models from Data
   • Chapter 7 Review, Test, and Projects

Appendix A: Review

• A.1 Algebra Essentials
• A.2 Geometry Essentials
• A.3 Factoring Polynomials; Completing the Square
• A.4 Solving Equations
• A.5 Complex Numbers; Quadratic Equations in the Complex Number System
• A.6 Interval Notation; Solving Inequalities
• A.7 nth Roots; Rational Exponents
• A.8 Lines

Appendix B: Graphing Utilities

• B.1 The Viewing Rectangle
• B.2 Using a Graphing Utility to Graph Equations
• B.3 Using a Graphing Utility to Locate Intercepts and Check for Symmetry
• B.4 Using a Graphing Utility to Solve Equations
• B.5 Square Screens
• B.6 Using a Graphing Utility to Graph Inequalities
• B.7 Using a Graphing Utility to Solve Systems of Linear Equations
• B.8 Using a Graphing Utility to Graph a Polar Equation
• B.9 Using a Graphing Utility to Graph Parametric Equations

For the Student

Prepare

• New – Integrated Review is now included in all Sullivan 11th Edition MyLab Math courses, including Precalculus, Algebra & Trigonometry, and Trigonometry. Integrated review can be used in corequisite courses, or simply to help students who enter without a full understanding of prerequisite skills and concepts.
• Integrated Review provides videos on review topics with a corresponding worksheets, along with premade, assignable skills-check quizzes and personalized review homework assignments.
• Algebra Review comprises four chapters of Intermediate Algebra—available within MyLab Math or as a printed supplement—that are ideal for a corequisite or a slower-paced course. In MyLab Math, videos  can be assigned to accompany the Algebra Review content are provided.

• New – Mindset material in MyLab Math encourages students to maintain a positive attitude about learning, value their own ability to grow, and view mistakes as learning opportunities — so often a major hurdle for math students.
• Just-in-time review begins all sections to prepare students for the topics ahead.

• Preparing for This Section lists previously learned concepts that will be useful in the section ahead. Page references are included for easy review.
• Now Work “Are You Prepared?” problems support the Preparing for This Section feature, allowing students to check that they are ready to proceed to the section ahead or if they need to turn back for further review. These problems appear at the start of each exercise set.

• All examples are clearly written and most conclude with a direction to Now Work, a related exercise, helping students to learn by doing.
• Showcase Examples provide how-to instruction by offering a guided, step-by-step approach to solving a problem. Students can immediately see how each of the steps in a problem is employed.
• Model It examples and exercises are now highlighted, making it easy to identify which exercises ask students to build a mathematical model from verbal descriptions or from data.
• New – Need to Review? is placed at the point of need for students. It provides a reference and page number to the discussion of a previous topic used in the current presentation.
• New – Graphing Images throughout each chapter show TI-84 Plus C and desmos screenshots. Using the graphing technology students are most familiar with, these images help students visualize concepts clearly and make stronger connections among equations, data and graphs in full color.
• Calculus icons appear next to information essential for the study of calculus. When the icon appears next to a definition, the notation used is consistent with that used in calculus.
• In Words provide alternative descriptions of select definitions and theorems, translating math into plain English.
• Warnings point out common mistakes and help students avoid them.

Practice

• Updated – Guided Lecture Notes ask students to complete definitions, procedures, and examples based on the content of the Author in Action videos and text. By directing students into essential material, students can focus and retain the most important concepts. These notes help increase the success of your students in any course structure.

• New – Guided Visualizations, powered by GeoGebra and created by Michael Sullivan III, help students visualize  concepts through directed exploration and purposeful manipulation. They are assignable in MyLab Math with assessment questions to check students’ conceptual understanding.

• Updated – Assess Your Understanding appears at the end of every section and contains a variety of problems for students to master the skills they need. Updated and expanded exercise sets appear throughout and a broader selection of STEM applications is reflected in examples and exercises throughout the text.
  
• “Are You Prepared?” problems appear at the start of every exercise set and help students determine exactly what they need to review and where to review it. This feature is referenced from the Preparing for This Section feature. Answers appear at the end of the section.
• Updated – Concepts and Vocabulary questions have been expanded to cover each objective. Theses questions are fill-in the-blank and true/false items that assess students’ understanding of key definitions and concepts. These have been written to serve as reading quizzes and are now assignable in MyLab Math .
• Updated – Skill Building problems provide straightforward practice, are organized by difficulty, and are correlated to section examples.
• Graphical problems use graphs in a variety of ways, supplementing students’ analytical understanding with graphical understanding.
• Mixed Practice problems offer comprehensive assessment of the skills learned in the section by asking questions that relate to more than one concept or objective. These problems may also require students to utilize skills learned in previous sections, helping them to see how concepts are tied together.
• Updated – Retain Your Knowledge exercises improve students’ recall of concepts learned earlier in the course. New for the 11th Edition, additional exercises are included that emphasize content students will build upon in the immediate upcoming section.
• Updated – Applications and Extensions allows students to apply their skills to real-world problems and to extend concepts learned in the section. These exercises have been updated and reflect the most current data available.
• New – Challenge Problems appear in most Exercise sets at the end of Applications and Extensions. Challenge Problems are thought-provoking and require some ingenuity to solve. They can be used for group work or to simply challenge your students.

Review

• New – College Algebra Essential Video Series covers the essential topics a college algebra student needs to understand to be successful in this course. Videos can be assigned in a MyLab Math homework assignment to remind students of the crucial content before students begin on their exercises.
• Review Exercises provide comprehensive review and practice of key skills, matched to the Learning Objectives for each section. These problems combine exercises from all sections, giving students comprehensive review in one place.
  
• Cumulative Review problem sets appear at the end of every chapter after Chapter 1. They combine problems from previous chapters, providing an ongoing cumulative review.
• Chapter Tests contain about 15-20 problems that can help students prepare for in-class exams. Chapter Test Prep Videos are available for additional help,
• Internet-based Chapter Projects, with assignable exercises in MyLab Math, enable students to learn by doing and have fun in the process. By exploring and considering a variety of carefully guided “what-if” scenarios, they will develop a better understanding of the concepts presented in the section. 

For the Instructor

• Updated – PowerPoints have been completely revised.  All textbook objectives are thoroughly covered and classroom examples in the PowerPoints differ from those found in the text.  A set of accessible PowerPoints are also available.
• Updated – Enhanced Sample Assignments in MyLab Mathuse a thoughtful mix of Sullivan hallmark practice problems that are geared to maximize students’ performance.
  
• New – Student & Assignment Tagging: The new tagging functionality in MyLab makes it easier for instructors to manage their courses, giving them flexibility to truly teach their course, their way. With student tagging functionality instructors may easily manage assignment delivery, communication and performance data by creating and adding students to tags.  With assignment tagging, instructors may also take action and manage settings for groups of assignments within a course.

Also available with MyLab Math 

MyLab™ Math is the teaching and learning platform that empowers you to reach every student. By combining trusted author content with digital tools and a flexible platform, MyLab Math personalizes the learning experience and improves results for each student. Learn more about MyLab Math.

Teach your course your way

• Flexible platform
• New – Student & Assignment Tagging: The new tagging functionality in MyLab makes it easier for instructors to manage their courses, giving them flexibility to truly teach their course, their way. With student tagging functionality instructors may easily manage assignment delivery, communication and performance data by creating and adding students to tags.  With assignment tagging, instructors may also take action and manage settings for groups of assignments within a course. 

• Preparedness
• New – Integrated Review is now included in all Sullivan 11th Edition MyLab Math courses, including Precalculus, Algebra & Trigonometry, and Trigonometry. Integrated review can be used in corequisite courses, or simply to help students who enter without a full understanding of prerequisite skills and concepts.
  
• Data & analysis
• Learning Catalytics™ helps instructors generate class discussion, guide their lectures, and promote peer-to-peer learning with real-time analytics. Now available through MyLab Math, Learning Catalytics is an interactive student response tool that uses students’ smartphones, tablets, or laptops to engage them in more sophisticated tasks and thinking.
• Michael Sullivan III has written Learning Catalytics questions to engage students in their course.

Empower each learner

• Personalized learning
• Motivation
• New – Mindset material in MyLab Math encourages students to maintain a positive attitude about learning, value their own ability to grow, and view mistakes as learning opportunities — so often a major hurdle for math students.
  

Deliver trusted content

• New – Guided Visualizations, created in GeoGebra by Michael Sullivan III, help students visualize the concept through directed exploration and purposeful manipulation. They are assignable in MyLab Math with assessment questions to check students’ conceptual understanding.
• Conceptual understanding
• Author in Action Videos are actual classroom lectures with fully worked-out examples presented by Michael Sullivan III. Video assessment questions are available to assign in MyLab Math for key Author in Action videos.

• Integrated Review is now included in all Sullivan 11th Edition MyLab Math courses, including Precalculus, Algebra & Trigonometry, and Trigonometry. Integrated review can be used in corequisite courses, or simply to help students who enter without a full understanding of prerequisite skills and concepts.

• Integrated Review provides videos on review topics with a corresponding worksheets, along with premade, assignable skills-check quizzes and personalized review homework assignments.
• Algebra Review comprises four chapters of Intermediate Algebra—available within MyLab Math or as a printed supplement—that are ideal for a corequisite or a slower-paced course. In MyLab Math, videos  can be assigned to accompany the Algebra Review content are provided.
• Need to Review? is now placed at the point of need for students. It provides a reference and page number to the discussion of a previous topic used in the current presentation.
• Mindset material content encourages students to maintain a positive attitude about learning, value their own ability to grow, and view mistakes as a learning opportunity — so often a major hurdle for math students.
• Graphing Images throughout each chapter show TI-84 Plus C and desmos screenshots. Using the graphing technology students are most familiar with, these images help students visualize concepts clearly and make stronger connections among equations, data and graphs in full color.
• Updated Guided Lecture Notes ask students to complete definitions, procedures, and examples based on the content of the Author in Action videos and book. By directing students into essential material, students can focus and retain the most important concepts. These notes help increase the success of your students in any course structure.
• Updated and expanded exercise sets appear throughout.
• Updated Applications and Extensions reflect the most current data available.
• Retain Your Knowledge exercises improve students’ recall of concepts learned earlier in the course. New for the 11th Edition, additional exercises are included that emphasize content students will build upon in the immediate upcoming section.
• Challenge Problems now appear in most Exercise sets at the end of Applications and Extensions. Challenge Problems are thought-provoking and require some ingenuity to solve. They can be used for group work or to challenge students.

Also available with MyLab Math

• Integrated Review version is now available for every title in the series. Integrated review can be used in corequisite courses, or simply to help students who enter without a full understanding of prerequisite skills and concepts.
• College Algebra Essential Video Series covers the essential topics a college algebra student needs to understand to be successful in this course.  Videos can be assigned in a MyLab Math homework assignment to remind students of the crucial content before students begin on their exercises.
  
• Guided Visualizations that help students better understand the visual aspects of key concepts in figure format. The figures are included in MyLab Math as both a teaching and an assignable learning tool.

Guided Lecture Notes ask students to complete definitions, procedures, and examples based on the content of the Author in Action videos and text. By directing students into essential material, students can focus and retain the most important concepts. These notes help increase the success of your students in any course structure.