Trigonometry: A Unit Circle Approach

✍ Scribed by Michael Sullivan

• Publisher: Pearson
• Year: 2015
• Tongue: English
• Leaves: 743
• Edition: 10
• Category: Library

✦ Synopsis

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Prepare. Practice. Review.

Mike Sullivan’s time-tested approach focuses students on the fundamental skills they need for the course: preparing for class, practicing with homework, and reviewing the concepts. The Tenth Edition has evolved to meet today’s course needs.

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✦ Table of Contents

Cover
Title Page
Copyright Page
Acknowledgments
Contents
Three Distinct Series
The Contemporary Series
Preface to the Instructor
Resources for Success
Applications Index
A
B
C
D
E
F
G
H
I
M
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1 Graphs and Functions
1.1 The Distance and Midpoint Formulas
Use the Distance Formula
Use the Midpoint Formula
1.2 Graphs of Equations in Two Variables; Circles
Graph Equations by Plotting Points
Find Intercepts from a Graph
Find Intercepts from an Equation
Test an Equation for Symmetry with Respect to the x-Axis, the y-Axis, and the Origin
Know How to Graph Key Equations
Write the Standard Form of the Equation of a Circle
Graph a Circle
Work with the General Form of the Equation of a Circle
1.3 Functions and Their Graphs
Determine Whether a Relation Represents a Function
Find the Value of a Function
Find the Difference Quotient of a Function
Find the Domain of a Function Defined by an Equation
Identify the Graph of a Function
Obtain Information from or about the Graph of a Function
1.4 Properties of Functions
Determine Even and Odd Functions from a Graph
Identify Even and Odd Functions from an Equation
Use a Graph to Determine Where a Function Is Increasing, Decreasing, or Constant
Use a Graph to Locate Local Maxima and Local Minima
Use a Graph to Locate the Absolute Maximum and the Absolute Minimum
Use a Graphing Utility to Approximate Local Maxima and Local Minima and to Determine Where a Function Is Increasing or Decreasing
Find the Average Rate of Change of a Function
1.5 Library of Functions; Piecewise-defined Functions
Graph the Functions Listed in the Library of Functions
Graph Piecewise-defined Functions
1.6 Graphing Techniques: Transformations
Graph Functions Using Vertical and Horizontal Shifts
Graph Functions Using Compressions and Stretches
Graph Functions Using Reflections about the x-Axis and the y-Axis
1.7 One-to-One Functions; Inverse Functions
Determine Whether a Function Is One-to-One
Determine the Inverse of a Function Defined by a Map or a Set of Ordered Pairs
Obtain the Graph of the Inverse Function from the Graph of the Function
Find the Inverse of a Function Defined by an Equation
Chapter Review
Chapter Test
Chapter Projects
2 Trigonometric Functions
2.1 Angles and Their Measure
Convert between Decimals and Degrees, Minutes, Seconds Measures for Angles
Find the Length of an Arc of a Circle
Convert from Degrees to Radians and from Radians to Degrees
Find the Area of a Sector of a Circle
Find the Linear Speed of an Object Traveling in Circular Motion
2.2 Trigonometric Functions: Unit Circle Approach
Find the Exact Values of the Trigonometric Functions Using a Point on the Unit Circle
Find the Exact Values of the Trigonometric Functions of Quadrantal Angles
Find the Exact Values of the Trigonometric Functions of ⎨/4 = 45°
Find the Exact Values of the Trigonometric Functions of ⎨/6 = 30° and ⎨/3 = 60°
Find the Exact Values of the Trigonometric Functions for Integer Multiples of ⎨/6 = 30°, ⎨/4 = 45°, and ⎨/3 = 60°
Use a Calculator to Approximate the Value of a Trigonometric Function
Use a Circle of Radius r to Evaluate the Trigonometric Functions
2.3 Properties of the Trigonometric Functions
Determine the Domain and the Range of the Trigonometric Functions
Determine the Period of the Trigonometric Functions
Determine the Signs of the Trigonometric Functions in a Given Quadrant
Find the Values of the Trigonometric Functions Using Fundamental Identities
Find the Exact Values of the Trigonometric Functions of an Angle Given One of the Functions and the Quadrant of the Angle
Use Even–Odd Properties to Find the Exact Values of the Trigonometric Functions
2.4 Graphs of the Sine and Cosine Functions
Graph Functions of the Form y = A sin (ωx) Using Transformations
Graph Functions of the Form y = A cos (ωx) Using Transformations
Determine the Amplitude and Period of Sinusoidal Functions
Graph Sinusoidal Functions Using Key Points
Find an Equation for a Sinusoidal Graph
2.5 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions
Graph Functions of the Form y = A tan (ωx) + B and y = A cot (ωx) + B
Graph Functions of the Form y = A csc (ωx) + B and y = A sec (ωx) + B
2.6 Phase Shift; Sinusoidal Curve Fitting
Graph Sinusoidal Functions of the Form y = A sin (ωx – ø) + B
Build Sinusoidal Models from Data
Chapter Review
Chapter Test
Cumulative Review
Chapter Projects
3 Analytic Trigonometry
3.1 The Inverse Sine, Cosine, and Tangent Functions
Find the Exact Value of an Inverse Sine Function
Find an Approximate Value of an Inverse Sine Function
Use Properties of Inverse Functions to Find Exact Values of Certain Composite Functions
Find the Inverse Function of a Trigonometric Function
Solve Equations Involving Inverse Trigonometric functions
3.2 The Inverse Trigonometric Functions (Continued)
Find the Exact Value of Expressions Involving the Inverse Sine, Cosine, and Tangent Functions
Define the Inverse Secant, Cosecant, and Cotangent Functions
Use a Calculator to Evaluate sec[sup(-1)] x, csc[sup(-1)] x, and cot[sup(-1)] x
Write a Trigonometric Expression as an Algebraic Expression
3.3 Trigonometric Equations
Solve Equations Involving a Single Trigonometric Function
Solve Trigonometric Equations Using a Calculator
Solve Trigonometric Equations Quadratic in Form
Solve Trigonometric Equations Using Fundamental Identities
Solve Trigonometric Equations Using a Graphing Utility
3.4 Trigonometric Identities
Use Algebra to Simplify Trigonometric Expressions
Establish Identities
3.5 Sum and Difference Formulas
Use Sum and Difference Formulas to Find Exact Values
Use Sum and Difference Formulas to Establish Identities
Use Sum and Difference Formulas Involving Inverse Trigonometric Functions
Solve Trigonometric Equations Linear in Sine and Cosine
3.6 Double-angle and Half-angle Formulas
Use Double-angle Formulas to Find Exact Values
Use Double-angle Formulas to Establish Identities
Use Half-angle Formulas to Find Exact Values
3.7 Product-to-Sum and Sum-to-Product Formulas
Express Products as Sums
Express Sums as Products
Chapter Review
Chapter Test
Cumulative Review
Chapter Projects
4 Applications of Trigonometric Functions
4.1 Right Triangle Trigonometry; Applications
Find the Value of Trigonometric Functions of Acute Angles Using Right Triangles
Use the Complementary Angle Theorem
Solve Right Triangles
Solve Applied Problems
4.2 The Law of Sines
Solve SAA or ASA Triangles
Solve SSA Triangles
Solve Applied Problems
4.3 The Law of Cosines
Solve SAS Triangles
Solve SSS Triangles
Solve Applied Problems
4.4 Area of a Triangle
Find the Area of SAS Triangles
Find the Area of SSS Triangles
4.5 Simple Harmonic Motion; Damped Motion; Combining Waves
Build a Model for an Object in Simple Harmonic Motion
Analyze Simple Harmonic Motion
Analyze an Object in Damped Motion
Graph the Sum of Two Functions
Chapter Review
Chapter Test
Cumulative Review
Chapter Projects
5 Polar Coordinates; Vectors
5.1 Polar Coordinates
Plot Points Using Polar Coordinates
Convert from Polar Coordinates to Rectangular Coordinates
Convert from Rectangular Coordinates to Polar Coordinates
Transform Equations between Polar and Rectangular Forms
5.2 Polar Equations and Graphs
Identify and Graph Polar Equations by Converting to Rectangular Equations
Test Polar Equations for Symmetry
Graph Polar Equations by Plotting Points
5.3 The Complex Plane; De Moivre's Theorem
Plot Points in the Complex Plane
Convert a Complex Number between Rectangular Form and Polar Form
Find Products and Quotients of Complex Numbers in Polar Form
Use De Moivre's Theorem
Find Complex Roots
5.4 Vectors
Graph Vectors
Find a Position Vector
Add and Subtract Vectors Algebraically
Find a Scalar Multiple and the Magnitude of a Vector
Find a Unit Vector
Find a Vector from Its Direction and Magnitude
Model with Vectors
5.5 The Dot Product
Find the Dot Product of Two Vectors
Find the Angle between Two Vectors
Determine Whether Two Vectors Are Parallel
Determine Whether Two Vectors Are Orthogonal
Decompose a Vector into Two Orthogonal Vectors
Compute Work
5.6 Vectors in Space
Find the Distance between Two Points in Space
Find Position Vectors in Space
Perform Operations on Vectors
Find the Dot Product
Find the Angle between Two Vectors
Find the Direction Angles of a Vector
5.7 The Cross Product
Find the Cross Product of Two Vectors
Know Algebraic Properties of the Cross Product
Know Geometric Properties of the Cross Product
Find a Vector Orthogonal to Two Given Vectors
Find the Area of a Parallelogram
Chapter Review
Chapter Test
Cumulative Review
Chapter Projects
6 Analytic Geometry
6.1 Conics
know the Names of the Conics
6.2 The Parabola
Analyze Parabolas with Vertex at the Origin
Analyze Parabolas with Vertex at (h, k)
Solve Applied Problems Involving Parabolas
6.3 The Ellipse
Analyze Ellipses with Center at the Origin
Analyze Ellipses with Center at (h, k)
Solve Applied Problems Involving Ellipses
6.4 The Hyperbola
Analyze Hyperbolas with Center at the Origin
Find the Asymptotes of a Hyperbola
Analyze Hyperbolas with Center at (h, k)
Solve Applied Problems Involving Hyperbolas
6.5 Rotation of Axes; General Form of a Conic
Identify a Conic
Use a Rotation of Axes to Transform Equations
Analyze an Equation Using a Rotation of Axes
Identify Conics without a Rotation of Axes
6.6 Polar Equations of Conics
Analyze and Graph Polar Equations of Conics
Convert the Polar Equation of a Conic to a Rectangular Equation
6.7 Plane Curves and Parametric Equations
Graph Parametric Equations
Find a Rectangular Equation for a Curve Defined Parametrically
Use Time as a Parameter in Parametric Equations
Find Parametric Equations for Curves Defined by Rectangular Equations
Chapter Review
Chapter Test
Cumulative Review
Chapter Projects
7 Exponential and Logarithmic Functions
7.1 Exponential Functions
Evaluate Exponential Functions
Graph Exponential Functions
Define the Number e
Solve Exponential Equations
7.2 Logarithmic Functions
Change Exponential Statements to Logarithmic Statements and Logarithmic Statements to Exponential Statements
Evaluate Logarithmic Expressions
Determine the Domain of a Logarithmic Function
Graph Logarithmic Functions
Solve Logarithmic Equations
7.3 Properties of Logarithms
Work with the Properties of Logarithms
Write a Logarithmic Expression as a Sum or Difference of Logarithms
Write a Logarithmic Expression as a Single Logarithm
Evaluate Logarithms Whose Base Is Neither 10 Nor e
7.4 Logarithmic and Exponential Equations
Solve Logarithmic Equations
Solve Exponential Equations
Solve Logarithmic and Exponential Equations Using a Graphing Utility
7.5 Financial Models
Determine the Future Value of a Lump Sum of Money
Calculate Effective Rates of Return
Determine the Present Value of a Lump Sum of Money
Determine the Rate of Interest or the Time Required to Double a Lump Sum of Money
7.6 Exponential Growth and Decay Models; Newton's Law; Logistic Growth and Decay Models
Find Equations of Populations That Obey the Law of Uninhibited Growth
Find Equations of Populations That Obey the Law of Decay
Use Newton's Law of Cooling
Use Logistic Models
7.7 Building Exponential, Logarithmic, and Logistic Models from Data
Build an Exponential Model from Data
Build a Logarithmic Model from Data
Build a Logistic Model from Data
Chapter Review
Chapter Test
Cumulative Review
Chapter Projects
Appendix A: Review
A.1 Algebra Essentials
Work with Sets
Graph Inequalities
Find Distance on the Real Number Line
Evaluate Algebraic Expressions
Determine the Domain of a Variable
Use the Laws of Exponents
Evaluate Square Roots
Use a Calculator to Evaluate Exponents
A.2 Geometry Essentials
Use the Pythagorean Theorem and Its Converse
Know Geometry Formulas
Understand Congruent Triangles and Similar Triangles
A.3 Factoring Polynomials; Completing the Square
Know Formulas for Special Products
Factor Polynomials
Complete the Square
A.4 Solving Equations
Solve Equations by Factoring
Solve Equations Involving Absolute Value
Solve a Quadratic Equation by Factoring
Solve a Quadratic Equation by Completing the Square
Solve a Quadratic Equation Using the Quadratic Formula
A.5 Complex Numbers; Quadratic Equations in the Complex Number System
Add, Subtract, Multiply, and Divide Complex Numbers
Solve Quadratic Equations in the Complex Number System
A.6 Interval Notation; Solving Inequalities
Use Interval Notation
Use Properties of Inequalities
Solve Inequalities
Solve Combined Inequalities
Solve Inequalities Involving Absolute Value
A.7 nth Roots; Rational Exponents
Work with nth Roots
Simplify Radicals
Rationalize Denominators
Solve Radical Equations
Simplify Expressions with Rational Exponents
A.8 Lines
Calculate and Interpret the Slope of a Line
Graph Lines Given a Point and the Slope
Find the Equation of a Vertical Line
Use the Point–Slope Form of a Line; Identify Horizontal Lines
Find the Equation of a Line Given Two Points
Write the Equation of a Line in Slope–Intercept Form
Identify the Slope and y-Intercept of a Line from Its Equation
Graph Lines Written in General Form Using Intercepts
Find Equations of Parallel Lines
Find Equations of Perpendicular Lines
A.9 Building Linear Models from Data
Draw and Interpret Scatter Diagrams
Distinguish between Linear and Nonlinear Relations
Use a Graphing Utility to Find the Line of Best Fit
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 a Polar Equation
B.7 Using a Graphing Utility to Graph Parametric Equations
Answers
Credits
Index
A
B
C
D
E
F
G
H
I
J
L
M
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X
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