Advanced Mathematics: Trigonometry and Pre-Calculus 2nd Edition Buy a Subscription Course Content Lessons Status 1 Introduction: Prerequisites for the Course – How to Use the Math Book – Expectations of Students 2 Lesson 61: Analyzing Single-Variable Data – What Is a Normal Distribution – Returning to “Box & Whisker” Plots 3 Lesson 62: Solving Abstract Equations – Defining Linear vs Direct Variation 4 Lesson 63: Using “Completing the Square” to Graph a Circle 5 Lesson 64: Graphing “Complex Numbers” in the Argand Plane, the Polar Form, and Sums & Products of Complex Numbers 6 Lesson 65: Working with Radicals in Trigonometric Functions and Sketching Graphs of Logarithm Functions 7 Lesson 66: Working with Formulas for Systems of Equations – Phase Shifts and Period Changes in Trigonometric Functions 8 Lesson 67: Defining What an “Antilogarithm” Is 9 Lesson 68: Defining the “Locus” of All Points in a Parabola – Equation of a Translated Parabola, Applications, & Derivations 10 Lesson 69: Defining a “Matrix” – Finding the Determinant in a Square Matrix 11 Lesson 70: Calculating Percentiles and “Z” Scores in Statistics 12 Lesson 71: First Circles, then Parabolas, now Ellipses (Part I) 13 Lesson 72: Solving Right Triangles – Using the “Law of Sines” to Solve for Unknown Parts of Triangles 14 Lesson 73: Solving Problems Involving Regular Polygons of Any Number of Sides, Inscribed in a Circle 15 Lesson 74: Using “Cramer’s Rule” to Solve a System of Linear Equations 16 Lesson 75: Combinations are Processed Differently than We Processed Permutations Earlier in the Textbook 17 Lesson 76: Graphing Functions of (- x) – Finding functions of the “Other Angle” – Trig Identities (Part I) – Making “Rules to Follow” 18 Lesson 77: Defining Binomial Expansion (Part I) 19 Lesson 78: Graphing the “Hyperbola” 20 Lesson 79: Using “De Moivre’s Theorem” – Finding Roots of Complex Numbers 21 Lesson 80: Trig Identities (Part II) 22 Lesson 81: Working with and Understanding the “Law of Cosines” 23 Lesson 82: Explaining How to “Take the Logarithm of a Number or an Expression” – Defining an “Exponential Equation” 24 Lesson 83: Defining “Simple Probability” – “Independent Events” and the Effects of “Replacement” in Probability 25 Lesson 84: Factoring “Factorable” Trig Expressions – Successfully Sketching Sinusoids 26 Lesson 85: Solving Advanced Trigonometric Equations – Solving “Clock” Word Problems 27 Lesson 86: Defining “Arithmetic Progressions” and the “Arithmetic Mean” 28 Lesson 87: Introducing “Sum & Difference” Trig Identities and “Tangent” Identities 29 Lesson 88: Working with “Growth & Decay” of Exponential Functions 30 Lesson 89: More on Ellipses (Part II) 31 Lesson 90: Introducing “Double-Angle” and “Half-Angle” Trig Identities 32 Lesson 91: Defining Geometric Expressions 33 Lesson 92: The Probability of “Mutually Exclusive Events” – Using Notations for Permutations or Combinations 34 Lesson 93: Working with Advanced Trigonometry Identities and Several Triangle Inequalities 35 Lesson 94: Graphing the Secant & Cosecant and then Graphing the Tangent & Cotangent 36 Lesson 95: Working with More Advanced Complex Roots 37 Lesson 96: More Work with Double-Angle Identities – Triangle Area Formulas Using the Sine Function – Working with a Proof of the “Law of Sines” – Equal Angles in Similar Triangles Implies Proportional Sides Among Them 38 Lesson 97: What is Meant by the “Ambiguous Case”? 39 Lesson 98: Finding a Logarithm to a Base Other Than “10” or “e” – Working with “Contrived Logarithm Problems” 40 Lesson 99: Using Different Notations for Different Sequences – Solving Advanced Sequence Problems – Finding the Arithmetic and Geometric Means 41 Lesson 100: Working with the Product of, and the Sum & Difference of, Trigonometric Identities 42 Lesson 101: More on Determinants – Evaluating Systems with and Without Determinants – Describing the Effects of Independent Equations in a Linear System 43 Lesson 102: More on Binomial Expansions (Part II) 44 Lesson 103: Doing Calculations Using Logarithms and Using Them to Calculate the pH (Relative Acidity) or H⁺ (Concentration of Hydrogen ions) 45 Lesson 104: Defining the Difference Between the Arithmetic and Geometric Series 46 Lesson 105: Defining “Cofactors” & Using Them to Evaluate Determinants 47 Lesson 106: Translation of a Conic Section – Recognizing the Difference Between the Equations of an Ellipse and a Hyperbola 48 Lesson 107: Describing a Convergent Geometric Series 49 Lesson 108: Learning How to Add and Multiply Matrices 50 Lesson 109: More Work with Rational Numbers 51 Lesson 110: Graphing the Arcsine & Arccosine, Arcsecant & Arccosecant, and the Arctangent & Arccotangent 52 Lesson 111: Working with Logarithmic Inequalities when the Base is “Less Than” or “Greater Than” 1 53 Lesson 112: Introduction to an Identity Called the “Binomial Theorem” 54 Lesson 113: Applying Synthetic Division Using a “Long Division Algorithm” – The Difference Between “Zeroes” and “Roots” 55 Lesson 114: Graphing Factored Polynomial Functions 56 Lesson 115: Applying the “Remainder Theorem” 57 Lesson 116: Defining the “Region of Interest” in a “Normalized Polynomial Equation” 58 Lesson 117: The Difference Between a “Prime Number” and “Relatively Prime Number” – Explanation and Application of the “Rational Roots Theorem” 59 Lesson 118: Finding the Roots of Polynomial Equations 60 Lesson 119: Using Descartes’ “Rule of Signs” – Applying the “Upper & Lower Bound” Theorem – Problems with Irrational Roots 61 Lesson 120: More About Matrices – Finding Inverse Matrices 62 Lesson 121: Writing the Equation of a “Piecewise” Function – Graphing the “Greatest Integer” Function 63 Lesson 122: Graphing Rational Functions – How Do You Graph a Function Whose Equation Has a Zero in the Denominator? 64 Lesson 123: Knowing of a General Equation to Describe All Conic sections 65 Lesson 124: Accurately Calculating the Coordinate Change when Using a “Point of Division” Formula 66 Lesson 125: Using the Texas Instrument Graphing Calculator (TI -82) to Graph – Solve Systems of Equations & Find Roots 67 Lesson 1: Working with “Real Numbers” and Review of Some Fundamental Algebraic Concepts 68 Lesson 2: More Review of Fundamental Algebraic Concepts – Using a Texas Instrument (TI-83) Graphing Calculator 69 Lesson 3: The Alternate Statement – The “Contrapositive” – Working with the “Converse,” Inverse,” and “If” Statements 70 Lesson 4: Measuring Angles in Radians – Using Trig Ratios – Signs of the “Four Quadrants” – Simplifying Trig Expressions 71 Lesson 5: A Review of Solving Various Word Problems 72 Lesson 6: Equations and Graphs of Functions – Using Functional Notation and Defining the Domain and Range of a Function 73 Lesson 7: Describing the “Unit Circle” – Defining of the “Centerline,” “Amplitude,” and “Phase Angle”of a Sinusoid – Describing What Is Meant by the “Period of a Trig Function” – Important Numbers in Mathematics – Working with Exponential Functions” 74 Lesson 8: Using the “Pythagorean Theorem” to Create “Pythagorean Trig Identities” – Negative Trig Identities & Even and Odd Trig Functions – Creating and Working with Trigonometric Identities – Trig Co-functions – Working with Similar Triangles 75 Lesson 9: Using the Absolute Value as the Distance – Working with “Special” Functions – A Review of Logarithms – Common vs Natural Logarithms – Solving Simple Logarithm Problems 76 Lesson 10: Working with Quadratic Polynomials and Their Equations & Functions – Applying the “Remainder Theorem” – A Review of Synthetic Division – Applying the “Rational Root Theorem” 77 Lesson 11: Continuity in Functions. – Identifying Left-Hand and Right-Hand Limits of Functions 78 Lesson 12: Working with Sum & Difference, Double-Angle & Half-Angle Trig Identities – More on Graphing Logarithm Functions 79 Lesson 13: Graphing Inverse Trig Functions – Solving Trigonometric Equations 80 Lesson 14: Introduction to Limits of Functions 81 Lesson 15: Introduction to “Interval Notation” & Products of Linear Factors – Tangent Lines – Describing “Increasing & Decreasing Functions” 82 Lesson 16: Finding Logarithms of Products & Quotients – Finding Logarithms of Powers – Solving Exponential Equations 83 Lesson 17: Describing Infinity as a Limit – Working with “Undefined Limits” 84 Lesson 18: Finding the Sums & Differences and Products & Quotients of Functions – Composing Functions 85 Lesson 19: Introduction to the “First Derivative” and its Notations – Finding Slopes of Curves 86 Lesson 20: Finding a Logarithm of a Base Other than “10” or “e” – Graphing Conics on a Graphing Calculator – or Not! 87 Lesson 21: Translations of Functions on Graphs – Graphing Rational Functions (Part I) 88 Lesson 22: Using the Binomial Theorem to Locate Specific Terms of a Binomial Expansion – Review of the Equations of the Five Types of Conic Sections 89 Lesson 23: Review of Trig Functions of nƟ – More Graphing of Conics Using a Graphing Calculator – or Not! 90 Lesson 24: Different Notations for Defining a First Derivative – Finding the First Derivative of x^n (x Raised to the nth Power) 91 Lesson 25: The Effects of the Constant-Multiple Rule for Derivatives – Defining the Derivatives of Sums & Differences – Working with the Proof of the Derivative of a Sum