Trigonometry: A Unit Circle Approach, 10th Edition

NOTE: Before purchasing, check with your instructor to ensure you select the correct ISBN. Several versions of Pearson's MyLab & Mastering products exist for each title, and registrations are not transferable. To register for and use Pearson's MyLab & Mastering products, you may also need a Course ID, which your instructor will provide. Used books, rentals, and purchases made outside of Pearson If purchasing or renting from companies other than Pearson, the access codes for Pearson's MyLab & Mastering products may not be included, may be incorrect, or may be previously redeemed. Check with the seller before completing your purchase. 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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If you would like to purchase both the physical text and MyMathLab, search for: 0321999320 / 9780321999320 Trigonometry Plus MyMathLab with eText -- Access Card Package Package consists of: 0321431308 / 9780321431301 MyMathLab -- Glue-in Access Card 0321654064 / 9780321654069 MyMathLab Inside Star Sticker 0321654064 / 9780321654069 MyMathLab Inside Star Sticker 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 N O P R S T V W 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 N O P Q R S T U V W X Y Z