| Three Distinct Series |
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xv | |
| The Contemporary Series |
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xvi | |
| Preface to the Instructor |
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xvii | |
| Resources for Success |
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xxii | |
| Applications Index |
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xxiv | |
| 1 Graphs and Functions |
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1 | (98) |
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1.1 The Distance and Midpoint Formulas |
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2 | (7) |
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1.2 Graphs of Equations in Two Variables; Circles |
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9 | (14) |
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Graph Equations by Plotting Points |
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Find Intercepts from a Graph |
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Find Intercepts from an Equation |
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Test an Equation for Symmetry with Respect to the x-Axis, the y-Axis, and the Origin |
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Know How to Graph Key Equations Write the Standard Form of the Equation of a Circle |
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Work with the General Form of the Equation of a Circle |
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1.3 Functions and Their Graphs |
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23 | (19) |
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Determine Whether a Relation Represents a Function |
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Find the Value of a Function |
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Find the Difference Quotient of a Function |
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Find the Domain of a Function Defined by an Equation |
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Identify the Graph of a Function |
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Obtain Information from or about the Graph of a Function |
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1.4 Properties of Functions |
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42 | (13) |
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Determine Even and Odd Functions from a Graph |
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Identify Even and Odd Functions from an Equation |
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Use a Graph to Determine Where a Function Is Increasing, Decreasing, or Constant |
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Use a Graph to Locate Local Maxima and Local Minima |
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Use a Graph to Locate the Absolute Maximum and the Absolute Minimum |
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Use a Graphing Utility to Approximate Local Maxima and Local Minima and to Determine Where a Function Is Increasing or Decreasing |
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Find the Average Rate of Change of a Function |
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1.5 Library of Functions; Piecewise-defined Functions |
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55 | (9) |
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Graph the Functions Listed in the Library of Functions |
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Graph Piecewise-defined Functions |
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1.6 Graphing Techniques: Transformations |
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64 | (14) |
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Graph Functions Using Vertical and Horizontal Shifts |
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Graph Functions Using Compressions and Stretches |
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Graph Functions Using Reflections about the x-Axis and the y-Axis |
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1.7 One-to-One Functions; Inverse Functions |
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78 | (13) |
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Determine Whether a Function Is One-to-One |
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Determine the Inverse of a Function Defined by a Map or a Set of Ordered Pairs |
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Obtain the Graph of the Inverse Function from the Graph of the Function |
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Find the Inverse of a Function Defined by an Equation |
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91 | (5) |
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96 | (1) |
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97 | (2) |
| 2 Trigonometric Functions |
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99 | (89) |
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2.1 Angles and Their Measure |
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100 | (14) |
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Convert between Decimals and Degrees, Minutes, Seconds Measures for Angles |
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Find the Length of an Arc of a Circle |
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Convert from Degrees to Radians and from Radians to Degrees |
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Find the Area of a Sector of a Circle |
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Find the Linear Speed of an Object Traveling in Circular Motion |
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2.2 Trigonometric Functions: Unit Circle Approach |
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114 | (17) |
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Find the Exact Values of the Trigonometric Functions Using a Point on the Unit Circle |
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Find the Exact Values of the Trigonometric Functions of Quadrantal Angles |
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Find the Exact Values of the Trigonometric Functions |
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Find the Exact Values of the Trigonometric Functions for Integer Multiples |
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Use a Calculator to Approximate the Value of a Trigonometric Function |
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Use a Circle of Radius r to Evaluate the Trigonometric Functions |
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2.3 Properties of the Trigonometric Functions |
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131 | (14) |
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Determine the Domain and the Range of the Trigonometric Functions |
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Determine the Period of the Trigonometric Functions |
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Determine the Signs of the Trigonometric Functions in a Given Quadrant |
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Find the Values of the Trigonometric Functions Using Fundamental Identities |
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Find the Exact Values of the Trigonometric Functions of an Angle Given One of the Functions and the Quadrant of the Angle |
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Use EvenOdd Properties to Find the Exact Values of the Trigonometric Functions |
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2.4 Graphs of the Sine and Cosine Functions |
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145 | (15) |
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Graph Functions of the Form y = A sin (cox) Using Transformations |
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Graph Functions of the Form y = A cos (wx) Using Transformations |
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Determine the Amplitude and Period of Sinusoidal Functions |
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Graph Sinusoidal Functions Using Key Points |
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Find an Equation for a Sinusoidal Graph |
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2.5 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions |
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160 | (8) |
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Graph Functions of the Form y = A tan (wx) + B and y = A cot (wx) + B |
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Graph Functions of the Form y = A csc (wx) + B and y = A sec (wx) + B |
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2.6 Phase Shift; Sinusoidal Curve Fitting |
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168 | (10) |
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Graph Sinusoidal Functions of the Form y = A sin (wx 4)) + B |
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Build Sinusoidal Models from Data |
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178 | (6) |
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184 | (1) |
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185 | (1) |
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186 | (2) |
| 3 Analytic Trigonometry |
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188 | (70) |
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3.1 The Inverse Sine, Cosine, and Tangent Functions |
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189 | (13) |
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Find the Exact Value of an Inverse Sine Function |
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Find an Approximate Value of an Inverse Sine Function |
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Use Properties of Inverse Functions to Find Exact Values of Certain Composite Functions |
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Find the Inverse Function of a Trigonometric Function |
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Solve Equations Involving Inverse Trigonometric Functions |
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3.2 The Inverse Trigonometric Functions (Continued) |
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202 | (6) |
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Find the Exact Value of Expressions Involving the Inverse Sine, Cosine, and Tangent Functions |
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Define the Inverse Secant, Cosecant, and Cotangent Functions |
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Use a Calculator to Evaluate sec-1 x, csc-1 x, and cot-1 x |
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Write a Trigonometric Expression as an Algebraic Expression |
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3.3 Trigonometric Equations |
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208 | (10) |
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Solve Equations Involving a Single Trigonometric Function |
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Solve Trigonometric Equations Using a Calculator |
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Solve Trigonometric Equations Quadratic in Form |
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Solve Trigonometric Equations Using Fundamental Identities |
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Solve Trigonometric Equations Using a Graphing Utility |
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3.4 Trigonometric Identities |
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218 | (8) |
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Use Algebra to Simplify Trigonometric Expressions |
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3.5 Sum and Difference Formulas |
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226 | (12) |
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Use Sum and Difference Formulas to Find Exact Values |
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Use Sum and Difference Formulas to Establish Identities |
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Use Sum and Difference Formulas Involving Inverse Trigonometric Functions |
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Solve Trigonometric Equations Linear in Sine and Cosine |
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3.6 Double-angle and Half-angle Formulas |
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238 | (10) |
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Use Double-angle Formulas to Find Exact Values |
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Use Double-angle Formulas to Establish Identities |
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Use Half-angle Formulas to Find Exact Values |
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3.7 Product-to-Sum and Sum-to-Product Formulas |
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248 | (4) |
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252 | (3) |
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255 | (1) |
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256 | (1) |
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257 | (1) |
| 4 Applications of Trigonometric Functions |
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258 | (53) |
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4.1 Right Triangle Trigonometry; Applications |
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259 | (13) |
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Find the Value of Trigonometric Functions of Acute Angles Using Right Triangles |
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Use the Complementary Angle Theorem |
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272 | (10) |
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Solve SAA or ASA Triangles |
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282 | (7) |
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289 | (6) |
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Find the Area of SAS Triangles |
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Find the Area of SSS Triangles |
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4.5 Simple Harmonic Motion; Damped Motion; Combining Waves |
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295 | (9) |
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Build a Model for an Object in Simple Harmonic Motion |
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Analyze Simple Harmonic Motion |
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Analyze an Object in Damped Motion |
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Graph the Sum of Two Functions |
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304 | (3) |
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307 | (1) |
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308 | (1) |
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309 | (2) |
| 5 Polar Coordinates; Vectors |
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311 | (75) |
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312 | (9) |
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Plot Points Using Polar Coordinates |
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Convert from Polar Coordinates to Rectangular Coordinates |
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Convert from Rectangular Coordinates to Polar Coordinates |
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Transform Equations between Polar and Rectangular Forms |
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5.2 Polar Equations and Graphs |
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321 | (15) |
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Identify and Graph Polar Equations by Converting to Rectangular Equations |
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Test Polar Equations for Symmetry |
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Graph Polar Equations by Plotting Points |
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5.3 The Complex Plane; De Moivre's Theorem |
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336 | (8) |
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Plot Points in the Complex Plane |
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Convert a Complex Number between Rectangular Form and Polar Form |
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Find Products and Quotients of Complex Numbers in Polar Form |
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344 | (14) |
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Add and Subtract Vectors Algebraically |
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Find a Scalar Multiple and the Magnitude of a Vector |
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Find a Vector from Its Direction and Magnitude |
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358 | (7) |
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Find the Dot Product of Two Vectors |
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Find the Angle between Two Vectors |
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Determine Whether Two Vectors Are Parallel |
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Determine Whether Two Vectors Are Orthogonal |
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Decompose a Vector into Two Orthogonal Vectors |
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365 | (10) |
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Find the Distance between Two Points in Space |
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Find Position Vectors in Space |
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Perform Operations on Vectors |
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Find the Angle between Two Vectors |
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Find the Direction Angles of a Vector |
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375 | (6) |
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Find the Cross Product of Two Vectors |
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Know Algebraic Properties of the Cross Product |
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Know Geometric Properties of the Cross Product |
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Find a Vector Orthogonal to Two Given Vectors |
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Find the Area of a Parallelogram |
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381 | (3) |
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384 | (1) |
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385 | (1) |
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385 | (1) |
| 6 Analytic Geometry |
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386 | (66) |
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387 | (1) |
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Know the Names of the Conics |
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388 | (9) |
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Analyze Parabolas with Vertex at the Origin |
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Analyze Parabolas with Vertex at (h, k) |
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Solve Applied Problems Involving Parabolas |
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397 | (10) |
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Analyze Ellipses with Center at the Origin |
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Analyze Ellipses with Center at (h, k) |
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Solve Applied Problems Involving Ellipses |
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407 | (13) |
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Analyze Hyperbolas with Center at the Origin |
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Find the Asymptotes of a Hyperbola |
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Analyze Hyperbolas with Center at (h, k) |
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Solve Applied Problems Involving Hyperbolas |
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6.5 Rotation of Axes; General Form of a Conic |
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420 | (8) |
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Use a Rotation of Axes to Transform Equations |
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Analyze an Equation Using a Rotation of Axes |
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Identify Conics without a Rotation of Axes |
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6.6 Polar Equations of Conics |
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428 | (6) |
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Analyze and Graph Polar Equations of Conics |
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Convert the Polar Equation of a Conic to a Rectangular Equation |
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6.7 Plane Curves and Parametric Equations |
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434 | (12) |
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Graph Parametric Equations |
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Find a Rectangular Equation for a Curve Defined Parametrically |
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Use Time as a Parameter in Parametric Equations |
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Find Parametric Equations for Curves Defined by Rectangular Equations |
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446 | (3) |
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449 | (1) |
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449 | (1) |
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450 | (2) |
| 7 Exponential and Logarithmic Functions |
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452 | |
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7.1 Exponential Functions |
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453 | (17) |
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Evaluate Exponential Functions |
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Graph Exponential Functions |
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Solve Exponential Equations |
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7.2 Logarithmic Functions |
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470 | (12) |
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Change Exponential Statements to Logarithmic Statements and Logarithmic Statements to Exponential Statements |
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Evaluate Logarithmic Expressions |
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Determine the Domain of a Logarithmic Function |
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Graph Logarithmic Functions |
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Solve Logarithmic Equations |
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7.3 Properties of Logarithms |
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482 | (9) |
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Work with the Properties of Logarithms |
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Write a Logarithmic Expression as a Sum or Difference of Logarithms |
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Write a Logarithmic Expression as a Single Logarithm |
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Evaluate Logarithms Whose Base Is Neither 10 Nor e |
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7.4 Logarithmic and Exponential Equations |
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491 | (7) |
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Solve Logarithmic Equations |
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Solve Exponential Equations |
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Solve Logarithmic and Exponential Equations Using a Graphing Utility |
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498 | (10) |
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Determine the Future Value of a Lump Sum of Money |
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Calculate Effective Rates of Return |
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Determine the Present Value of a Lump Sum of Money |
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Determine the Rate of Interest or the Time Required to Double a Lump Sum of Money |
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7.6 Exponential Growth and Decay Models; Newton's Law; Logistic Growth and Decay Models |
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508 | (11) |
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Find Equations of Populations That Obey the Law of Uninhibited Growth |
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Find Equations of Populations That Obey the Law of Decay |
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Use Newton's Law of Cooling |
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7.7 Building Exponential, Logarithmic, and Logistic Models from Data |
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519 | (7) |
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Build an Exponential Model from Data |
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Build a Logarithmic Model from Data |
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Build a Logistic Model from Data |
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526 | (4) |
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530 | (1) |
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531 | (1) |
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532 | |
| Appendix A Review |
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A1 | |
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A1 | |
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Find Distance on the Real Number Line |
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Evaluate Algebraic Expressions |
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Determine the Domain of a Variable |
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Use the Laws of Exponents |
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Use a Calculator to Evaluate Exponents |
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A14 | |
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Use the Pythagorean Theorem and Its Converse |
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Understand Congruent Triangles and Similar Triangles |
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A.3 Factoring Polynomials; Completing the Square |
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A22 | |
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Know Formulas for Special Products |
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A27 | |
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Solve Equations by Factoring |
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Solve Equations Involving Absolute Value |
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Solve a Quadratic Equation by Factoring |
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Solve a Quadratic Equation by Completing the Square |
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Solve a Quadratic Equation Using the Quadratic Formula |
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A.5 Complex Numbers; Quadratic Equations in the Complex Number System |
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A37 | |
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Add, Subtract, Multiply, and Divide Complex Numbers |
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Solve Quadratic Equations in the Complex Number System |
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A.6 Interval Notation; Solving Inequalities |
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A46 | |
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Use Properties of Inequalities |
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Solve Combined Inequalities |
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Solve Inequalities Involving Absolute Value |
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A.7 nth Roots; Rational Exponents |
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A56 | |
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Simplify Expressions with Rational Exponents |
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A64 | |
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Calculate and Interpret the Slope of a Line |
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Graph Lines Given a Point and the Slope |
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Find the Equation of a Vertical Line |
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Use the PointSlope Form of a Line; Identify Horizontal Lines |
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Find the Equation of a Line Given Two Points |
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Write the Equation of a Line in SlopeIntercept Form |
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Identify the Slope and y-Intercept of a Line from Its Equation |
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Graph Lines Written in General Form Using Intercepts |
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Find Equations of Parallel Lines |
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Find Equations of Perpendicular Lines |
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A.9 Building Linear Models from Data |
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A79 | |
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Draw and Interpret Scatter Diagrams |
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Distinguish between Linear and Nonlinear Relations |
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Use a Graphing Utility to Find the Line of Best Fit |
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| Appendix B Graphing Utilities |
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B1 | |
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B.1 The Viewing Rectangle |
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B1 | |
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B.2 Using a Graphing Utility to Graph Equations |
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B3 | |
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B.3 Using a Graphing Utility to Locate Intercepts and Check for Symmetry |
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B5 | |
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B.4 Using a Graphing Utility to Solve Equations |
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B6 | |
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B8 | |
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B.6 Using a Graphing Utility to Graph a Polar Equation |
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B9 | |
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B.7 Using a Graphing Utility to Graph Parametric Equations |
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B9 | |
| Answers |
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AN1 | |
| Credits |
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C1 | |
| Index |
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I1 | |
