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| Introduction | |
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| Review of Numbers and Coordinate Systems | |
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| Review of numbers, including natural, whole, integers, zero, rational, irrational, real, complex, and imaginary numbers | |
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| Absolute value | |
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| Significant digits and rounding numbers and decimals | |
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| Review of coordinate systems, including two- and three-dimensional rectangular coordinates, polar coordinates, cylindrical coordinates, and spherical coordinates | |
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| Chapter 1 summary and highlights | |
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| Review of Geometry | |
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| Introduction | |
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| Lines and angles | |
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| Triangles | |
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| Polygons and quadrilaterals | |
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| Conic sections, including circles, arcs and angles, ellipses, parabolas, and hyperbolas | |
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| Three-dimensional objects, including cubes, rectangular solids, cylinders, spheres, cones, and pyramids | |
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| Chapter 2 summary and highlights | |
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| Triangles and Trigonometric Functions | |
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| Right triangles and the trigonometric functions | |
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| Solving right triangles | |
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| Examples and applications of right triangles | |
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| Oblique triangles and the Law of Sines and Law of Cosines | |
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| Solving oblique triangles | |
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| Examples and applications of oblique triangles | |
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| Finding the area of a triangle | |
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| Chapter 3 summary and highlights | |
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| Trigonometric Functions in a Coordinate System and Circular Functions | |
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| Review of functions and their properties | |
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| Types of functions, including composite, inverse, linear, nonlinear, even, odd, exponential, logarithmic, identity, absolute value, squaring, cubing, square root, cube root, reciprocal, and functions with more than one variable | |
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| Coordinate systems, radians, degrees, and arc length | |
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| Angles in standard position and coterminal angles | |
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| The trigonometric functions defined in a coordinate system in standard position, quadrant signs, and quadrantal angles | |
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| Reference angles and reference triangles | |
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| Native angles | |
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| Reciprocal functions and cofunction relationships | |
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| Circular functions and the unit circle | |
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| Linear and angular velocity | |
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| Chapter 4 summary and highlights | |
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| Graphs of Trigonometric and Circular Functions and their Periodic Nature | |
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| Circular motion | |
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| Graphs of sine and cosine | |
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| Transforming graphs of sine and cosine through changes in amplitude, period, and vertical and horizontal shifting | |
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| Applications of sinusoids | |
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| Graphs of secant and cosecant | |
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| Graphs of tangent and cotangent | |
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| Chapter 5 summary and highlights | |
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| Inverse Trigonometric Functions | |
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| Review of general inverse functions | |
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| Inverse trigonometric functions | |
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| Inverse sine and inverse cosine | |
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| Inverse tangent | |
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| Inverse cotangent, inverse secant, and inverse cosecant | |
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| Chapter 6 summary and highlights | |
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| Trigonometric Identities | |
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| Summary of identities | |
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| Quotient identities and reciprocal identities | |
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| Pythagorean identities | |
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| Negative number/angle identities | |
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| Verifying trigonometric identities | |
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| Sum and difference of angles/numbers identities, also called addition and subtraction identities | |
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| Cofunction identities | |
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| Supplementary angle relations | |
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| Double-angle/number identities | |
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| Half-angle identities | |
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| Product-to-sum identities | |
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| Sum/difference-to-product identities | |
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| Squared formulas | |
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| Chapter 7 summary and highlights | |
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| Trigonometric Functions in Equations and Inequalities | |
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| Review of solving algebraic equations | |
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| Review of solving algebraic quadratic equations | |
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| Review of solving algebraic inequalities | |
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| Solving algebraic equations and inequalities using graphing | |
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| Introduction to solving trigonometric equations and inequalities | |
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| Solving simple trigonometric equations using standard position angles, reference triangles, and identities | |
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| Solving trigonometric equations involving powers using factoring, a unit circle, and identities | |
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| Solving trigonometric equations and inequalities using the quadratic formula, identities, unit circles, factoring, and graphing | |
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| Estimating solutions to trigonometric equations and inequalities using graphing | |
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| Chapter 8 summary and highlights | |
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| Trigonometric Functions and Vectors | |
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| Definitions of vectors | |
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| Representing vectors in terms of their components in a coordinate system | |
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| Representing vectors in terms of their components in a coordinate system using the unit vectors i, j, and k | |
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| Addition and subtraction of vectors | |
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| Simple vector problems | |
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| Multiplying a vector with a scalar | |
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| Dot or scalar products | |
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| Vector or cross product | |
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| Chapter 9 summary and highlights | |
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| Trigonometric Functions In Polar Coordinates and Equations, and Parametric Equations | |
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| Polar coordinates defined | |
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| Converting between rectangular and polar coordinate systems and equations | |
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| Graphing polar equations | |
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| Parametric equations | |
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| Chapter 10 summary and highlights | |
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| Complex Numbers and The Complex Plane | |
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| Complex numbers defined | |
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| The complex plane in rectangular form | |
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| Addition and subtraction of complex numbers in rectangular form | |
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| Complex numbers in polar form and the complex plane | |
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| Converting between rectangular and polar form | |
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| Multiplication and division of complex numbers in rectangular and polar forms | |
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| Powers and roots of complex numbers | |
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| Chapter 11 summary and highlights | |
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| Relationships Between Trigonometric Functions, Exponential Functions, Hyperbolic Functions and Series Expansions | |
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| Relationships between trigonometric and exponential functions | |
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| Background: summary of sequences, progressions and series, and expanding a function into a series | |
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| Hyperbolic functions | |
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| Chapter 12 summary and highlights | |
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| Spherical Trigonometry | |
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| Definitions and properties | |
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| Measuring spherical triangles | |
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| The Law of Sines and the Law of Cosines for spherical triangles for calculating sides and angles | |
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| Celestial sphere | |
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| Chapter 13 summary and highlights | |
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| Index | |