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Algebra and Trigonometry

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Algebra and TrigonometryIndex
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Table of contents
  1. Preface
  2. 1 Prerequisites
    1. Introduction to Prerequisites
    2. 1.1 Real Numbers: Algebra Essentials
    3. 1.2 Exponents and Scientific Notation
    4. 1.3 Radicals and Rational Exponents
    5. 1.4 Polynomials
    6. 1.5 Factoring Polynomials
    7. 1.6 Rational Expressions
    8. Chapter Review
      1. Key Terms
      2. Key Equations
      3. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  3. 2 Equations and Inequalities
    1. Introduction to Equations and Inequalities
    2. 2.1 The Rectangular Coordinate Systems and Graphs
    3. 2.2 Linear Equations in One Variable
    4. 2.3 Models and Applications
    5. 2.4 Complex Numbers
    6. 2.5 Quadratic Equations
    7. 2.6 Other Types of Equations
    8. 2.7 Linear Inequalities and Absolute Value Inequalities
    9. Chapter Review
      1. Key Terms
      2. Key Equations
      3. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  4. 3 Functions
    1. Introduction to Functions
    2. 3.1 Functions and Function Notation
    3. 3.2 Domain and Range
    4. 3.3 Rates of Change and Behavior of Graphs
    5. 3.4 Composition of Functions
    6. 3.5 Transformation of Functions
    7. 3.6 Absolute Value Functions
    8. 3.7 Inverse Functions
    9. Chapter Review
      1. Key Terms
      2. Key Equations
      3. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  5. 4 Linear Functions
    1. Introduction to Linear Functions
    2. 4.1 Linear Functions
    3. 4.2 Modeling with Linear Functions
    4. 4.3 Fitting Linear Models to Data
    5. Chapter Review
      1. Key Terms
      2. Key Concepts
    6. Exercises
      1. Review Exercises
      2. Practice Test
  6. 5 Polynomial and Rational Functions
    1. Introduction to Polynomial and Rational Functions
    2. 5.1 Quadratic Functions
    3. 5.2 Power Functions and Polynomial Functions
    4. 5.3 Graphs of Polynomial Functions
    5. 5.4 Dividing Polynomials
    6. 5.5 Zeros of Polynomial Functions
    7. 5.6 Rational Functions
    8. 5.7 Inverses and Radical Functions
    9. 5.8 Modeling Using Variation
    10. Chapter Review
      1. Key Terms
      2. Key Equations
      3. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  7. 6 Exponential and Logarithmic Functions
    1. Introduction to Exponential and Logarithmic Functions
    2. 6.1 Exponential Functions
    3. 6.2 Graphs of Exponential Functions
    4. 6.3 Logarithmic Functions
    5. 6.4 Graphs of Logarithmic Functions
    6. 6.5 Logarithmic Properties
    7. 6.6 Exponential and Logarithmic Equations
    8. 6.7 Exponential and Logarithmic Models
    9. 6.8 Fitting Exponential Models to Data
    10. Chapter Review
      1. Key Terms
      2. Key Equations
      3. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  8. 7 The Unit Circle: Sine and Cosine Functions
    1. Introduction to The Unit Circle: Sine and Cosine Functions
    2. 7.1 Angles
    3. 7.2 Right Triangle Trigonometry
    4. 7.3 Unit Circle
    5. 7.4 The Other Trigonometric Functions
    6. Chapter Review
      1. Key Terms
      2. Key Equations
      3. Key Concepts
    7. Exercises
      1. Review Exercises
      2. Practice Test
  9. 8 Periodic Functions
    1. Introduction to Periodic Functions
    2. 8.1 Graphs of the Sine and Cosine Functions
    3. 8.2 Graphs of the Other Trigonometric Functions
    4. 8.3 Inverse Trigonometric Functions
    5. Chapter Review
      1. Key Terms
      2. Key Equations
      3. Key Concepts
    6. Exercises
      1. Review Exercises
      2. Practice Test
  10. 9 Trigonometric Identities and Equations
    1. Introduction to Trigonometric Identities and Equations
    2. 9.1 Verifying Trigonometric Identities and Using Trigonometric Identities to Simplify Trigonometric Expressions
    3. 9.2 Sum and Difference Identities
    4. 9.3 Double-Angle, Half-Angle, and Reduction Formulas
    5. 9.4 Sum-to-Product and Product-to-Sum Formulas
    6. 9.5 Solving Trigonometric Equations
    7. Chapter Review
      1. Key Terms
      2. Key Equations
      3. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  11. 10 Further Applications of Trigonometry
    1. Introduction to Further Applications of Trigonometry
    2. 10.1 Non-right Triangles: Law of Sines
    3. 10.2 Non-right Triangles: Law of Cosines
    4. 10.3 Polar Coordinates
    5. 10.4 Polar Coordinates: Graphs
    6. 10.5 Polar Form of Complex Numbers
    7. 10.6 Parametric Equations
    8. 10.7 Parametric Equations: Graphs
    9. 10.8 Vectors
    10. Chapter Review
      1. Key Terms
      2. Key Equations
      3. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  12. 11 Systems of Equations and Inequalities
    1. Introduction to Systems of Equations and Inequalities
    2. 11.1 Systems of Linear Equations: Two Variables
    3. 11.2 Systems of Linear Equations: Three Variables
    4. 11.3 Systems of Nonlinear Equations and Inequalities: Two Variables
    5. 11.4 Partial Fractions
    6. 11.5 Matrices and Matrix Operations
    7. 11.6 Solving Systems with Gaussian Elimination
    8. 11.7 Solving Systems with Inverses
    9. 11.8 Solving Systems with Cramer's Rule
    10. Chapter Review
      1. Key Terms
      2. Key Equations
      3. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  13. 12 Analytic Geometry
    1. Introduction to Analytic Geometry
    2. 12.1 The Ellipse
    3. 12.2 The Hyperbola
    4. 12.3 The Parabola
    5. 12.4 Rotation of Axes
    6. 12.5 Conic Sections in Polar Coordinates
    7. Chapter Review
      1. Key Terms
      2. Key Equations
      3. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  14. 13 Sequences, Probability, and Counting Theory
    1. Introduction to Sequences, Probability and Counting Theory
    2. 13.1 Sequences and Their Notations
    3. 13.2 Arithmetic Sequences
    4. 13.3 Geometric Sequences
    5. 13.4 Series and Their Notations
    6. 13.5 Counting Principles
    7. 13.6 Binomial Theorem
    8. 13.7 Probability
    9. Chapter Review
      1. Key Terms
      2. Key Equations
      3. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  15. A | Proofs, Identities, and Toolkit Functions
  16. Answer Key
    1. Chapter 1
    2. Chapter 2
    3. Chapter 3
    4. Chapter 4
    5. Chapter 5
    6. Chapter 6
    7. Chapter 7
    8. Chapter 8
    9. Chapter 9
    10. Chapter 10
    11. Chapter 11
    12. Chapter 12
    13. Chapter 13
  17. Index
A
AAS (angle-angle-side) 10.1 Non-right Triangles: Law of Sines
absolute maximum 3.3 Rates of Change and Behavior of Graphs
absolute minimum 3.3 Rates of Change and Behavior of Graphs
absolute value 3.2 Domain and Range, 3.6 Absolute Value Functions
absolute value equation 2.6 Other Types of Equations, 2.6 Other Types of Equations
absolute value function 3.2 Domain and Range
absolute value functions 3.6 Absolute Value Functions, 3.6 Absolute Value Functions
absolute value inequality 2.7 Linear Inequalities and Absolute Value Inequalities, 2.7 Linear Inequalities and Absolute Value Inequalities
addition method 11.1 Systems of Linear Equations: Two Variables, 11.1 Systems of Linear Equations: Two Variables, 11.1 Systems of Linear Equations: Two Variables
Addition Principle 13.5 Counting Principles
addition property 2.7 Linear Inequalities and Absolute Value Inequalities
adjacent side 7.2 Right Triangle Trigonometry
algebraic expression 1.1 Real Numbers: Algebra Essentials
altitude 10.1 Non-right Triangles: Law of Sines
ambiguous case 10.1 Non-right Triangles: Law of Sines
amplitude 8.1 Graphs of the Sine and Cosine Functions
angle 7.1 Angles
angle of depression 7.2 Right Triangle Trigonometry
angle of elevation 7.2 Right Triangle Trigonometry, 10.1 Non-right Triangles: Law of Sines
angle of rotation 12.4 Rotation of Axes
angular speed 7.1 Angles, 7.1 Angles
annual interest 13.4 Series and Their Notations
annual percentage rate (APR) 6.1 Exponential Functions
annuity 13.4 Series and Their Notations
apoapsis 12.5 Conic Sections in Polar Coordinates
arc 7.1 Angles
arc length 7.1 Angles, 7.1 Angles, 7.3 Unit Circle
arccosine 8.3 Inverse Trigonometric Functions
Archimedes’ spiral 10.4 Polar Coordinates: Graphs
arcsine 8.3 Inverse Trigonometric Functions
arctangent 8.3 Inverse Trigonometric Functions
area 2.3 Models and Applications
area of a circle 5.2 Power Functions and Polynomial Functions
area of a sector 7.1 Angles
argument 10.5 Polar Form of Complex Numbers
arithmetic sequence 13.2 Arithmetic Sequences, 13.2 Arithmetic Sequences, 13.2 Arithmetic Sequences, 13.2 Arithmetic Sequences, 13.4 Series and Their Notations
arithmetic series 13.4 Series and Their Notations
arrow notation 5.6 Rational Functions
associative property of addition 1.1 Real Numbers: Algebra Essentials
associative property of multiplication 1.1 Real Numbers: Algebra Essentials
asymptotes 12.2 The Hyperbola
augmented matrix 11.6 Solving Systems with Gaussian Elimination, 11.6 Solving Systems with Gaussian Elimination, 11.6 Solving Systems with Gaussian Elimination, 11.7 Solving Systems with Inverses
average rate of change 3.3 Rates of Change and Behavior of Graphs
axes of symmetry 12.2 The Hyperbola
axis of symmetry 5.1 Quadratic Functions, 5.1 Quadratic Functions, 12.3 The Parabola, 12.3 The Parabola
B
base 1.1 Real Numbers: Algebra Essentials
binomial 1.4 Polynomials, 5.4 Dividing Polynomials
binomial coefficient 13.6 Binomial Theorem
binomial expansion 13.6 Binomial Theorem, 13.6 Binomial Theorem
Binomial Theorem 13.6 Binomial Theorem
break-even point 11.1 Systems of Linear Equations: Two Variables
C
cardioid 10.4 Polar Coordinates: Graphs
carrying capacity 6.7 Exponential and Logarithmic Models
Cartesian coordinate system 2.1 The Rectangular Coordinate Systems and Graphs
Cartesian equation 10.3 Polar Coordinates
Celsius 3.7 Inverse Functions
center of a hyperbola 12.2 The Hyperbola
center of an ellipse 12.1 The Ellipse
central rectangle 12.2 The Hyperbola
change-of-base formula 6.5 Logarithmic Properties, 6.5 Logarithmic Properties
circle 11.3 Systems of Nonlinear Equations and Inequalities: Two Variables, 11.3 Systems of Nonlinear Equations and Inequalities: Two Variables
circular motion 8.1 Graphs of the Sine and Cosine Functions
circumference 7.1 Angles
co-vertex 12.1 The Ellipse
co-vertices 12.1 The Ellipse
coefficient 1.4 Polynomials, 1.4 Polynomials, 5.2 Power Functions and Polynomial Functions, 5.5 Zeros of Polynomial Functions
coefficient matrix 11.6 Solving Systems with Gaussian Elimination, 11.6 Solving Systems with Gaussian Elimination, 11.7 Solving Systems with Inverses, 11.7 Solving Systems with Inverses
cofunction 9.2 Sum and Difference Identities
cofunction identities 7.2 Right Triangle Trigonometry, 9.2 Sum and Difference Identities
column 11.5 Matrices and Matrix Operations
column matrix 11.5 Matrices and Matrix Operations
combinations 13.5 Counting Principles, 13.6 Binomial Theorem
combining functions 3.4 Composition of Functions
common base 6.6 Exponential and Logarithmic Equations
common difference 13.2 Arithmetic Sequences, 13.4 Series and Their Notations
common logarithm 6.3 Logarithmic Functions
common ratio 13.3 Geometric Sequences, 13.4 Series and Their Notations
commutative 3.4 Composition of Functions
commutative property of addition 1.1 Real Numbers: Algebra Essentials
commutative property of multiplication 1.1 Real Numbers: Algebra Essentials
complement of an event 13.7 Probability
completing the square 2.5 Quadratic Equations, 2.5 Quadratic Equations
complex conjugate 2.4 Complex Numbers
Complex Conjugate Theorem 5.5 Zeros of Polynomial Functions
complex number 2.4 Complex Numbers, 10.5 Polar Form of Complex Numbers
complex plane 2.4 Complex Numbers, 10.5 Polar Form of Complex Numbers
composite function 3.4 Composition of Functions
composition of functions 3.4 Composition of Functions
compound inequality 2.7 Linear Inequalities and Absolute Value Inequalities
compound interest 6.1 Exponential Functions
compression 4.1 Linear Functions, 6.2 Graphs of Exponential Functions, 6.4 Graphs of Logarithmic Functions
conditional equation 2.2 Linear Equations in One Variable
conic 12.1 The Ellipse, 12.2 The Hyperbola, 12.5 Conic Sections in Polar Coordinates
conic section 12.4 Rotation of Axes
conic sections 10.6 Parametric Equations
conjugate axis 12.2 The Hyperbola
consistent system 11.1 Systems of Linear Equations: Two Variables
constant 1.1 Real Numbers: Algebra Essentials
constant function 3.2 Domain and Range
constant of variation 5.8 Modeling Using Variation, 5.8 Modeling Using Variation
continuous 5.3 Graphs of Polynomial Functions
continuous function 5.2 Power Functions and Polynomial Functions
convex limaçons 10.4 Polar Coordinates: Graphs
coordinate plane 12.3 The Parabola
correlation coefficient 4.3 Fitting Linear Models to Data
cosecant 7.4 The Other Trigonometric Functions, 8.2 Graphs of the Other Trigonometric Functions
cosecant function 8.2 Graphs of the Other Trigonometric Functions, 8.2 Graphs of the Other Trigonometric Functions, 8.2 Graphs of the Other Trigonometric Functions, 9.1 Verifying Trigonometric Identities and Using Trigonometric Identities to Simplify Trigonometric Expressions
cosine 9.4 Sum-to-Product and Product-to-Sum Formulas, 9.4 Sum-to-Product and Product-to-Sum Formulas
cosine function 7.3 Unit Circle, 8.1 Graphs of the Sine and Cosine Functions, 8.1 Graphs of the Sine and Cosine Functions, 8.1 Graphs of the Sine and Cosine Functions, 8.1 Graphs of the Sine and Cosine Functions, 8.1 Graphs of the Sine and Cosine Functions
cost function 3.4 Composition of Functions, 11.1 Systems of Linear Equations: Two Variables
cotangent 7.4 The Other Trigonometric Functions, 8.2 Graphs of the Other Trigonometric Functions
cotangent function 8.2 Graphs of the Other Trigonometric Functions, 9.1 Verifying Trigonometric Identities and Using Trigonometric Identities to Simplify Trigonometric Expressions
coterminal angles 7.1 Angles, 7.1 Angles
Cramer’s Rule 11.8 Solving Systems with Cramer's Rule, 11.8 Solving Systems with Cramer's Rule, 11.8 Solving Systems with Cramer's Rule, 11.8 Solving Systems with Cramer's Rule
cube root 5.2 Power Functions and Polynomial Functions
cubic functions 5.7 Inverses and Radical Functions
curvilinear path 10.6 Parametric Equations
D
De Moivre 10.5 Polar Form of Complex Numbers
De Moivre’s Theorem 10.5 Polar Form of Complex Numbers, 10.5 Polar Form of Complex Numbers
decompose a composite function 3.4 Composition of Functions
decomposition 11.4 Partial Fractions
decreasing function 3.3 Rates of Change and Behavior of Graphs, 4.1 Linear Functions
decreasing linear function 4.1 Linear Functions
degenerate conic sections 12.4 Rotation of Axes
degree 1.4 Polynomials, 1.4 Polynomials, 5.2 Power Functions and Polynomial Functions, 7.1 Angles
dependent system 11.1 Systems of Linear Equations: Two Variables, 11.1 Systems of Linear Equations: Two Variables, 11.2 Systems of Linear Equations: Three Variables
dependent variable 3.1 Functions and Function Notation
Descartes 10.5 Polar Form of Complex Numbers
Descartes’ Rule of Signs 5.5 Zeros of Polynomial Functions
determinant 11.8 Solving Systems with Cramer's Rule, 11.8 Solving Systems with Cramer's Rule, 11.8 Solving Systems with Cramer's Rule
difference of squares 1.4 Polynomials
dimpled limaçons 10.4 Polar Coordinates: Graphs
direct variation 5.8 Modeling Using Variation, 5.8 Modeling Using Variation
directrix 12.3 The Parabola, 12.3 The Parabola, 12.3 The Parabola, 12.3 The Parabola, 12.3 The Parabola, 12.5 Conic Sections in Polar Coordinates, 12.5 Conic Sections in Polar Coordinates, 12.5 Conic Sections in Polar Coordinates, 12.5 Conic Sections in Polar Coordinates, 12.5 Conic Sections in Polar Coordinates
discriminant 2.5 Quadratic Equations, 2.5 Quadratic Equations
displacement 7.1 Angles
distance formula 2.1 The Rectangular Coordinate Systems and Graphs, 9.2 Sum and Difference Identities, 12.2 The Hyperbola, 12.3 The Parabola
distributive property 1.1 Real Numbers: Algebra Essentials
diverges 13.4 Series and Their Notations
dividend 5.4 Dividing Polynomials
Division Algorithm 5.4 Dividing Polynomials, 5.5 Zeros of Polynomial Functions
divisor 5.4 Dividing Polynomials
domain 3.1 Functions and Function Notation, 3.1 Functions and Function Notation, 3.2 Domain and Range, 3.2 Domain and Range, 3.2 Domain and Range, 3.2 Domain and Range, 8.3 Inverse Trigonometric Functions, 8.3 Inverse Trigonometric Functions
domain and range 3.2 Domain and Range, 3.2 Domain and Range
domain of a composite function 3.4 Composition of Functions
dot product 10.8 Vectors
double-angle formulas 9.3 Double-Angle, Half-Angle, and Reduction Formulas, 9.3 Double-Angle, Half-Angle, and Reduction Formulas
doubling time 6.7 Exponential and Logarithmic Models
Dürer 10.4 Polar Coordinates: Graphs
E
eccentricity 12.5 Conic Sections in Polar Coordinates, 12.5 Conic Sections in Polar Coordinates
electrostatic force 3.3 Rates of Change and Behavior of Graphs
elimination 11.3 Systems of Nonlinear Equations and Inequalities: Two Variables
ellipse 10.7 Parametric Equations: Graphs, 10.7 Parametric Equations: Graphs, 11.3 Systems of Nonlinear Equations and Inequalities: Two Variables, 12.1 The Ellipse, 12.1 The Ellipse, 12.1 The Ellipse, 12.1 The Ellipse, 12.1 The Ellipse, 12.3 The Parabola, 12.5 Conic Sections in Polar Coordinates, 12.5 Conic Sections in Polar Coordinates
ellipsis 13.1 Sequences and Their Notations
end behavior 5.2 Power Functions and Polynomial Functions, 5.6 Rational Functions
endpoint 3.3 Rates of Change and Behavior of Graphs, 7.1 Angles
entry 11.5 Matrices and Matrix Operations
equation 1.1 Real Numbers: Algebra Essentials, 3.1 Functions and Function Notation
equation in quadratic form 2.6 Other Types of Equations
equation in two variables 2.1 The Rectangular Coordinate Systems and Graphs
Euler 10.5 Polar Form of Complex Numbers
even function 3.5 Transformation of Functions, 9.1 Verifying Trigonometric Identities and Using Trigonometric Identities to Simplify Trigonometric Expressions
even-odd identities 9.1 Verifying Trigonometric Identities and Using Trigonometric Identities to Simplify Trigonometric Expressions, 9.1 Verifying Trigonometric Identities and Using Trigonometric Identities to Simplify Trigonometric Expressions
event 13.7 Probability
experiment 13.7 Probability
explicit formula 13.1 Sequences and Their Notations, 13.1 Sequences and Their Notations, 13.1 Sequences and Their Notations, 13.2 Arithmetic Sequences, 13.3 Geometric Sequences
exponent 1.1 Real Numbers: Algebra Essentials
Exponential decay 6.1 Exponential Functions, 6.1 Exponential Functions, 6.2 Graphs of Exponential Functions, 6.7 Exponential and Logarithmic Models, 6.7 Exponential and Logarithmic Models, 6.7 Exponential and Logarithmic Models, 6.8 Fitting Exponential Models to Data
exponential equation 6.6 Exponential and Logarithmic Equations
exponential function 6.1 Exponential Functions
exponential growth 6.1 Exponential Functions, 6.1 Exponential Functions, 6.2 Graphs of Exponential Functions, 6.7 Exponential and Logarithmic Models, 6.7 Exponential and Logarithmic Models, 6.7 Exponential and Logarithmic Models
exponential notation 1.1 Real Numbers: Algebra Essentials
extraneous solution 6.6 Exponential and Logarithmic Equations
extraneous solutions 2.6 Other Types of Equations
extrapolation 4.3 Fitting Linear Models to Data
F
factor by grouping 1.5 Factoring Polynomials
Factor Theorem 5.5 Zeros of Polynomial Functions
factorial 13.1 Sequences and Their Notations
factoring 2.5 Quadratic Equations
Fahrenheit 3.7 Inverse Functions
feasible region 11.3 Systems of Nonlinear Equations and Inequalities: Two Variables
finite arithmetic sequence 13.2 Arithmetic Sequences
finite sequence 13.1 Sequences and Their Notations
foci 12.1 The Ellipse, 12.1 The Ellipse, 12.1 The Ellipse, 12.2 The Hyperbola
focus 12.1 The Ellipse, 12.3 The Parabola, 12.3 The Parabola, 12.3 The Parabola, 12.3 The Parabola, 12.3 The Parabola, 12.5 Conic Sections in Polar Coordinates, 12.5 Conic Sections in Polar Coordinates, 12.5 Conic Sections in Polar Coordinates, 12.5 Conic Sections in Polar Coordinates
FOIL 1.4 Polynomials
formula 1.1 Real Numbers: Algebra Essentials, 3.1 Functions and Function Notation
function 3.1 Functions and Function Notation, 3.2 Domain and Range
function notation 3.1 Functions and Function Notation
Fundamental Counting Principle 13.5 Counting Principles
Fundamental Theorem of Algebra 5.5 Zeros of Polynomial Functions, 5.5 Zeros of Polynomial Functions
G
Gauss 10.5 Polar Form of Complex Numbers, 11.2 Systems of Linear Equations: Three Variables, 11.6 Solving Systems with Gaussian Elimination
Gaussian elimination 11.2 Systems of Linear Equations: Three Variables, 11.6 Solving Systems with Gaussian Elimination, 11.6 Solving Systems with Gaussian Elimination
general form 5.1 Quadratic Functions
general form of a quadratic function 5.1 Quadratic Functions
Generalized Pythagorean Theorem 10.2 Non-right Triangles: Law of Cosines
geometric sequence 13.3 Geometric Sequences, 13.4 Series and Their Notations
geometric series 13.4 Series and Their Notations
global maximum 5.3 Graphs of Polynomial Functions, 5.3 Graphs of Polynomial Functions
global minimum 5.3 Graphs of Polynomial Functions, 5.3 Graphs of Polynomial Functions
graph in two variables 2.1 The Rectangular Coordinate Systems and Graphs
gravity 10.7 Parametric Equations: Graphs
greatest common factor 1.5 Factoring Polynomials, 1.5 Factoring Polynomials, 2.5 Quadratic Equations
H
half-angle formulas 9.3 Double-Angle, Half-Angle, and Reduction Formulas, 9.3 Double-Angle, Half-Angle, and Reduction Formulas
half-life 6.6 Exponential and Logarithmic Equations, 6.7 Exponential and Logarithmic Models
Heaviside method 11.4 Partial Fractions
Heron of Alexandria 10.2 Non-right Triangles: Law of Cosines
Heron’s formula 10.2 Non-right Triangles: Law of Cosines
horizontal asymptote 5.6 Rational Functions, 5.6 Rational Functions, 5.6 Rational Functions
horizontal compression 3.5 Transformation of Functions, 9.5 Solving Trigonometric Equations
horizontal line 2.2 Linear Equations in One Variable, 4.1 Linear Functions, 4.1 Linear Functions
horizontal line test 3.1 Functions and Function Notation
horizontal reflection 3.5 Transformation of Functions
horizontal shift 3.5 Transformation of Functions, 6.2 Graphs of Exponential Functions, 6.4 Graphs of Logarithmic Functions, 8.1 Graphs of the Sine and Cosine Functions
horizontal stretch 3.5 Transformation of Functions
hyperbola 12.2 The Hyperbola, 12.2 The Hyperbola, 12.2 The Hyperbola, 12.2 The Hyperbola, 12.2 The Hyperbola, 12.2 The Hyperbola, 12.2 The Hyperbola, 12.2 The Hyperbola, 12.3 The Parabola, 12.5 Conic Sections in Polar Coordinates, 12.5 Conic Sections in Polar Coordinates
hypotenuse 7.2 Right Triangle Trigonometry
I
identities 7.4 The Other Trigonometric Functions
identity equation 2.2 Linear Equations in One Variable
identity matrix 11.7 Solving Systems with Inverses, 11.7 Solving Systems with Inverses, 11.7 Solving Systems with Inverses
identity property of addition 1.1 Real Numbers: Algebra Essentials
identity property of multiplication 1.1 Real Numbers: Algebra Essentials
imaginary number 2.4 Complex Numbers
inconsistent equation 2.2 Linear Equations in One Variable
inconsistent system 11.1 Systems of Linear Equations: Two Variables, 11.1 Systems of Linear Equations: Two Variables, 11.2 Systems of Linear Equations: Three Variables
increasing function 3.3 Rates of Change and Behavior of Graphs, 4.1 Linear Functions
increasing linear function 4.1 Linear Functions
independent system 11.1 Systems of Linear Equations: Two Variables
independent variable 3.1 Functions and Function Notation
index 1.3 Radicals and Rational Exponents, 1.3 Radicals and Rational Exponents
index of summation 13.4 Series and Their Notations
inequality 11.3 Systems of Nonlinear Equations and Inequalities: Two Variables
infinite geometric sequence 13.4 Series and Their Notations
infinite sequence 13.1 Sequences and Their Notations
infinite series 13.4 Series and Their Notations
initial point 10.8 Vectors, 10.8 Vectors
initial side 7.1 Angles
inner-loop limaçons 10.4 Polar Coordinates: Graphs
input 3.1 Functions and Function Notation
integers 1.1 Real Numbers: Algebra Essentials, 1.1 Real Numbers: Algebra Essentials
intercepts 2.1 The Rectangular Coordinate Systems and Graphs
Intermediate Value Theorem 5.3 Graphs of Polynomial Functions, 5.3 Graphs of Polynomial Functions
interpolation 4.3 Fitting Linear Models to Data
intersection 13.7 Probability
interval 2.7 Linear Inequalities and Absolute Value Inequalities
interval notation 2.7 Linear Inequalities and Absolute Value Inequalities, 3.2 Domain and Range, 3.3 Rates of Change and Behavior of Graphs
inverse cosine function 8.3 Inverse Trigonometric Functions
inverse function 3.7 Inverse Functions, 5.7 Inverses and Radical Functions
inverse matrix 11.7 Solving Systems with Inverses, 11.7 Solving Systems with Inverses
inverse of a radical function 5.7 Inverses and Radical Functions
inverse of a rational function 5.7 Inverses and Radical Functions
inverse property of addition 1.1 Real Numbers: Algebra Essentials
inverse property of multiplication 1.1 Real Numbers: Algebra Essentials
inverse sine function 8.3 Inverse Trigonometric Functions
inverse tangent function 8.3 Inverse Trigonometric Functions
inverse trigonometric functions 8.3 Inverse Trigonometric Functions, 8.3 Inverse Trigonometric Functions, 8.3 Inverse Trigonometric Functions, 8.3 Inverse Trigonometric Functions
inverse variation 5.8 Modeling Using Variation
inverse variations 5.8 Modeling Using Variation
inversely proportional 5.8 Modeling Using Variation
invertible functions 5.7 Inverses and Radical Functions
invertible matrix 11.7 Solving Systems with Inverses, 11.8 Solving Systems with Cramer's Rule
irrational numbers 1.1 Real Numbers: Algebra Essentials, 1.1 Real Numbers: Algebra Essentials
J
joint variation 5.8 Modeling Using Variation
K
Kronecker 10.5 Polar Form of Complex Numbers
L
latus rectum 12.3 The Parabola, 12.3 The Parabola, 12.3 The Parabola, 12.3 The Parabola
Law of Cosines 10.2 Non-right Triangles: Law of Cosines, 10.2 Non-right Triangles: Law of Cosines
Law of Sines 10.1 Non-right Triangles: Law of Sines, 10.2 Non-right Triangles: Law of Cosines
leading coefficient 1.4 Polynomials, 1.4 Polynomials, 5.2 Power Functions and Polynomial Functions
leading term 1.4 Polynomials, 1.4 Polynomials, 5.2 Power Functions and Polynomial Functions
least common denominator 1.6 Rational Expressions, 2.2 Linear Equations in One Variable
least squares regression 4.3 Fitting Linear Models to Data
lemniscate 10.4 Polar Coordinates: Graphs
linear equation 2.2 Linear Equations in One Variable
Linear Factorization Theorem 5.5 Zeros of Polynomial Functions, 5.5 Zeros of Polynomial Functions
linear function 4.1 Linear Functions, 4.1 Linear Functions
linear growth 6.1 Exponential Functions
linear model 4.2 Modeling with Linear Functions, 4.3 Fitting Linear Models to Data
linear relationship 4.3 Fitting Linear Models to Data
linear speed 7.1 Angles
local extrema 3.3 Rates of Change and Behavior of Graphs
local maximum 3.3 Rates of Change and Behavior of Graphs, 5.3 Graphs of Polynomial Functions
local minimum 3.3 Rates of Change and Behavior of Graphs, 5.3 Graphs of Polynomial Functions
logarithm 6.3 Logarithmic Functions
logarithmic equation 6.6 Exponential and Logarithmic Equations
logarithmic model 6.8 Fitting Exponential Models to Data
logistic growth model 6.7 Exponential and Logarithmic Models
long division 5.4 Dividing Polynomials
lower limit of summation 13.4 Series and Their Notations
M
magnitude 3.2 Domain and Range, 3.5 Transformation of Functions, 10.5 Polar Form of Complex Numbers, 10.8 Vectors
main diagonal 11.6 Solving Systems with Gaussian Elimination
major and minor axes 12.1 The Ellipse
major axis 12.1 The Ellipse, 12.1 The Ellipse
matrix 11.5 Matrices and Matrix Operations, 11.5 Matrices and Matrix Operations, 11.6 Solving Systems with Gaussian Elimination
matrix multiplication 11.5 Matrices and Matrix Operations, 11.7 Solving Systems with Inverses, 11.7 Solving Systems with Inverses
matrix operations 11.5 Matrices and Matrix Operations
maximum value 5.1 Quadratic Functions
measure of an angle 7.1 Angles
midline 8.1 Graphs of the Sine and Cosine Functions
midpoint formula 2.1 The Rectangular Coordinate Systems and Graphs
minimum value 5.1 Quadratic Functions
minor axis 12.1 The Ellipse
model breakdown 4.3 Fitting Linear Models to Data
modulus 3.2 Domain and Range, 10.5 Polar Form of Complex Numbers
monomial 1.4 Polynomials
Multiplication Principle 13.5 Counting Principles
multiplication property 2.7 Linear Inequalities and Absolute Value Inequalities
multiplicative inverse 11.7 Solving Systems with Inverses, 11.7 Solving Systems with Inverses
multiplicative inverse of a matrix 11.7 Solving Systems with Inverses, 11.7 Solving Systems with Inverses
multiplicity 5.3 Graphs of Polynomial Functions, 5.3 Graphs of Polynomial Functions
mutually exclusive events 13.7 Probability
N
n factorial 13.1 Sequences and Their Notations
natural logarithm 6.3 Logarithmic Functions, 6.6 Exponential and Logarithmic Equations
natural numbers 1.1 Real Numbers: Algebra Essentials, 1.1 Real Numbers: Algebra Essentials, 3.1 Functions and Function Notation
negative angle 7.1 Angles
Newton’s Law of Cooling 6.7 Exponential and Logarithmic Models
nominal rate 6.1 Exponential Functions
non-right triangles 10.1 Non-right Triangles: Law of Sines
nondegenerate conic sections 12.4 Rotation of Axes
nonlinear inequality 11.3 Systems of Nonlinear Equations and Inequalities: Two Variables
nth partial sum 13.4 Series and Their Notations
nth root of a complex number 10.5 Polar Form of Complex Numbers
nth term of the sequence 13.1 Sequences and Their Notations, 13.1 Sequences and Their Notations
O
oblique triangle 10.1 Non-right Triangles: Law of Sines
odd function 3.5 Transformation of Functions, 9.1 Verifying Trigonometric Identities and Using Trigonometric Identities to Simplify Trigonometric Expressions
one-loop limaçon 10.4 Polar Coordinates: Graphs
one-to-one 6.2 Graphs of Exponential Functions, 6.3 Logarithmic Functions, 6.5 Logarithmic Properties, 6.5 Logarithmic Properties
one-to-one function 3.1 Functions and Function Notation, 3.7 Inverse Functions, 8.3 Inverse Trigonometric Functions
opposite side 7.2 Right Triangle Trigonometry
order of magnitude 6.7 Exponential and Logarithmic Models
order of operations 1.1 Real Numbers: Algebra Essentials
ordered pair 2.1 The Rectangular Coordinate Systems and Graphs, 3.1 Functions and Function Notation, 3.2 Domain and Range
ordered triple 11.2 Systems of Linear Equations: Three Variables
origin 2.1 The Rectangular Coordinate Systems and Graphs, 3.6 Absolute Value Functions
outcomes 13.7 Probability
output 3.1 Functions and Function Notation
P
parabola 5.1 Quadratic Functions, 5.1 Quadratic Functions, 10.7 Parametric Equations: Graphs, 11.3 Systems of Nonlinear Equations and Inequalities: Two Variables, 12.3 The Parabola, 12.3 The Parabola, 12.3 The Parabola, 12.3 The Parabola, 12.3 The Parabola, 12.5 Conic Sections in Polar Coordinates, 12.5 Conic Sections in Polar Coordinates, 12.5 Conic Sections in Polar Coordinates
parallel 2.2 Linear Equations in One Variable
parallel lines 4.1 Linear Functions, 4.1 Linear Functions
parallelograms 10.8 Vectors
parameter 10.6 Parametric Equations
parametric equations 10.6 Parametric Equations, 10.7 Parametric Equations: Graphs, 10.7 Parametric Equations: Graphs
parametric form 10.7 Parametric Equations: Graphs
parent function 6.4 Graphs of Logarithmic Functions
partial fraction 11.4 Partial Fractions
partial fraction decomposition 11.4 Partial Fractions, 11.4 Partial Fractions
Pascal 10.4 Polar Coordinates: Graphs
Pascal's Triangle 13.6 Binomial Theorem
perfect square trinomial 1.4 Polynomials
periapsis 12.5 Conic Sections in Polar Coordinates
perimeter 2.3 Models and Applications
period 7.4 The Other Trigonometric Functions, 8.1 Graphs of the Sine and Cosine Functions, 8.2 Graphs of the Other Trigonometric Functions, 8.2 Graphs of the Other Trigonometric Functions, 9.5 Solving Trigonometric Equations
periodic function 8.1 Graphs of the Sine and Cosine Functions
permutation 13.5 Counting Principles
perpendicular 2.2 Linear Equations in One Variable
perpendicular lines 4.1 Linear Functions, 4.1 Linear Functions
pH 6.5 Logarithmic Properties
phase shift 8.1 Graphs of the Sine and Cosine Functions
piecewise function 3.2 Domain and Range
piecewise functions 13.1 Sequences and Their Notations
point-slope form 4.1 Linear Functions
point-slope formula 2.2 Linear Equations in One Variable, 12.2 The Hyperbola
polar axis 10.3 Polar Coordinates
polar coordinates 10.3 Polar Coordinates, 10.3 Polar Coordinates, 10.3 Polar Coordinates, 10.4 Polar Coordinates: Graphs
polar equation 10.3 Polar Coordinates, 10.4 Polar Coordinates: Graphs, 10.4 Polar Coordinates: Graphs, 12.5 Conic Sections in Polar Coordinates
polar form 10.5 Polar Form of Complex Numbers
polar form of a complex number 10.5 Polar Form of Complex Numbers
polar form of a conic 12.5 Conic Sections in Polar Coordinates
polar grid 10.3 Polar Coordinates, 10.3 Polar Coordinates
pole 10.3 Polar Coordinates
polynomial 1.4 Polynomials, 1.4 Polynomials, 5.5 Zeros of Polynomial Functions
polynomial equation 2.6 Other Types of Equations
polynomial function 5.2 Power Functions and Polynomial Functions, 5.3 Graphs of Polynomial Functions, 5.3 Graphs of Polynomial Functions, 5.3 Graphs of Polynomial Functions
position vector 10.8 Vectors, 10.8 Vectors
positive angle 7.1 Angles
power function 5.2 Power Functions and Polynomial Functions
power rule for logarithms 6.5 Logarithmic Properties, 6.5 Logarithmic Properties
principal nth root 1.3 Radicals and Rational Exponents, 1.3 Radicals and Rational Exponents
principal square root 1.3 Radicals and Rational Exponents, 1.3 Radicals and Rational Exponents
probability 13.7 Probability
probability model 13.7 Probability
product of two matrices 11.5 Matrices and Matrix Operations
product rule for logarithms 6.5 Logarithmic Properties, 6.5 Logarithmic Properties
product-to-sum formulas 9.4 Sum-to-Product and Product-to-Sum Formulas, 9.4 Sum-to-Product and Product-to-Sum Formulas
profit function 11.1 Systems of Linear Equations: Two Variables
properties of determinants 11.8 Solving Systems with Cramer's Rule
Proxima Centauri 6.7 Exponential and Logarithmic Models
Pythagoras 10.5 Polar Form of Complex Numbers
Pythagorean identities 9.1 Verifying Trigonometric Identities and Using Trigonometric Identities to Simplify Trigonometric Expressions, 9.1 Verifying Trigonometric Identities and Using Trigonometric Identities to Simplify Trigonometric Expressions
Pythagorean identity 9.2 Sum and Difference Identities
Pythagorean Identity 7.3 Unit Circle, 7.3 Unit Circle, 7.4 The Other Trigonometric Functions
Pythagorean Theorem 2.1 The Rectangular Coordinate Systems and Graphs, 2.5 Quadratic Equations, 9.3 Double-Angle, Half-Angle, and Reduction Formulas, 9.5 Solving Trigonometric Equations, 10.2 Non-right Triangles: Law of Cosines, 10.7 Parametric Equations: Graphs
Q
quadrant 2.1 The Rectangular Coordinate Systems and Graphs
quadrantal angle 7.1 Angles
quadratic 11.4 Partial Fractions, 11.4 Partial Fractions
quadratic equation 2.5 Quadratic Equations, 2.5 Quadratic Equations, 2.5 Quadratic Equations, 2.5 Quadratic Equations, 9.5 Solving Trigonometric Equations
quadratic formula 2.5 Quadratic Equations, 2.5 Quadratic Equations, 2.5 Quadratic Equations, 9.5 Solving Trigonometric Equations
quadratic function 5.1 Quadratic Functions, 5.1 Quadratic Functions
quotient 5.4 Dividing Polynomials
quotient identities 9.1 Verifying Trigonometric Identities and Using Trigonometric Identities to Simplify Trigonometric Expressions, 9.1 Verifying Trigonometric Identities and Using Trigonometric Identities to Simplify Trigonometric Expressions
quotient rule for logarithms 6.5 Logarithmic Properties
R
radian 7.1 Angles, 7.1 Angles, 7.1 Angles
radian measure 7.1 Angles
radical 1.3 Radicals and Rational Exponents, 1.3 Radicals and Rational Exponents
radical equation 2.6 Other Types of Equations
radical expression 1.3 Radicals and Rational Exponents, 1.3 Radicals and Rational Exponents
Radical expressions 1.3 Radicals and Rational Exponents
radical functions 5.7 Inverses and Radical Functions
radicand 1.3 Radicals and Rational Exponents, 1.3 Radicals and Rational Exponents, 2.6 Other Types of Equations
radiocarbon dating 6.7 Exponential and Logarithmic Models
range 3.1 Functions and Function Notation, 8.3 Inverse Trigonometric Functions
rate of change 3.3 Rates of Change and Behavior of Graphs, 4.2 Modeling with Linear Functions
rational equation 2.2 Linear Equations in One Variable
rational expression 1.6 Rational Expressions, 2.2 Linear Equations in One Variable, 11.4 Partial Fractions, 11.4 Partial Fractions, 11.4 Partial Fractions
rational function 5.6 Rational Functions, 5.6 Rational Functions, 5.6 Rational Functions
rational number 2.2 Linear Equations in One Variable
rational numbers 1.1 Real Numbers: Algebra Essentials, 1.1 Real Numbers: Algebra Essentials
Rational Zero Theorem 5.5 Zeros of Polynomial Functions, 5.5 Zeros of Polynomial Functions
ray 7.1 Angles
real number line 1.1 Real Numbers: Algebra Essentials
real numbers 1.1 Real Numbers: Algebra Essentials
reciprocal 2.2 Linear Equations in One Variable, 3.7 Inverse Functions, 5.2 Power Functions and Polynomial Functions
reciprocal function 5.6 Rational Functions
reciprocal identities 9.1 Verifying Trigonometric Identities and Using Trigonometric Identities to Simplify Trigonometric Expressions, 9.1 Verifying Trigonometric Identities and Using Trigonometric Identities to Simplify Trigonometric Expressions
reciprocal identity 8.2 Graphs of the Other Trigonometric Functions, 8.2 Graphs of the Other Trigonometric Functions
rectangular coordinates 10.3 Polar Coordinates, 10.3 Polar Coordinates, 10.3 Polar Coordinates
rectangular equation 10.3 Polar Coordinates, 10.6 Parametric Equations
rectangular form 10.5 Polar Form of Complex Numbers, 10.7 Parametric Equations: Graphs
recursive formula 13.1 Sequences and Their Notations, 13.2 Arithmetic Sequences, 13.2 Arithmetic Sequences, 13.3 Geometric Sequences
reduction formulas 9.3 Double-Angle, Half-Angle, and Reduction Formulas, 9.3 Double-Angle, Half-Angle, and Reduction Formulas
reference angle 7.1 Angles, 7.3 Unit Circle, 7.4 The Other Trigonometric Functions
reflection 6.2 Graphs of Exponential Functions, 6.4 Graphs of Logarithmic Functions
regression analysis 6.8 Fitting Exponential Models to Data, 6.8 Fitting Exponential Models to Data, 6.8 Fitting Exponential Models to Data
regression line 4.3 Fitting Linear Models to Data
relation 3.1 Functions and Function Notation
remainder 5.4 Dividing Polynomials
Remainder Theorem 5.5 Zeros of Polynomial Functions
removable discontinuity 5.6 Rational Functions, 5.6 Rational Functions
Restricting the domain 3.7 Inverse Functions
resultant 10.8 Vectors
revenue function 11.1 Systems of Linear Equations: Two Variables
Richter Scale 6.3 Logarithmic Functions
right triangle 7.2 Right Triangle Trigonometry, 8.3 Inverse Trigonometric Functions
roots 5.1 Quadratic Functions
rose curve 10.4 Polar Coordinates: Graphs
row 11.5 Matrices and Matrix Operations
row matrix 11.5 Matrices and Matrix Operations
row operations 11.6 Solving Systems with Gaussian Elimination, 11.6 Solving Systems with Gaussian Elimination, 11.6 Solving Systems with Gaussian Elimination, 11.7 Solving Systems with Inverses, 11.7 Solving Systems with Inverses, 11.7 Solving Systems with Inverses, 11.7 Solving Systems with Inverses
row-echelon form 11.6 Solving Systems with Gaussian Elimination, 11.6 Solving Systems with Gaussian Elimination, 11.6 Solving Systems with Gaussian Elimination
row-equivalent 11.6 Solving Systems with Gaussian Elimination
S
sample space 13.7 Probability
SAS (side-angle-side) triangle 10.2 Non-right Triangles: Law of Cosines
scalar 10.8 Vectors, 11.5 Matrices and Matrix Operations
scalar multiple 10.8 Vectors, 11.5 Matrices and Matrix Operations
Scalar multiplication 10.8 Vectors, 11.5 Matrices and Matrix Operations
scatter plot 4.3 Fitting Linear Models to Data
scientific notation 1.2 Exponents and Scientific Notation, 1.2 Exponents and Scientific Notation, 1.2 Exponents and Scientific Notation
secant 7.4 The Other Trigonometric Functions, 8.2 Graphs of the Other Trigonometric Functions
secant function 8.2 Graphs of the Other Trigonometric Functions
sector of a circle 7.1 Angles
sequence 13.1 Sequences and Their Notations, 13.1 Sequences and Their Notations, 13.2 Arithmetic Sequences
series 13.4 Series and Their Notations
set-builder notation 2.7 Linear Inequalities and Absolute Value Inequalities, 3.2 Domain and Range
sigma 13.4 Series and Their Notations
sine 9.1 Verifying Trigonometric Identities and Using Trigonometric Identities to Simplify Trigonometric Expressions, 9.4 Sum-to-Product and Product-to-Sum Formulas, 9.4 Sum-to-Product and Product-to-Sum Formulas
sine function 7.3 Unit Circle, 8.1 Graphs of the Sine and Cosine Functions, 8.1 Graphs of the Sine and Cosine Functions, 8.1 Graphs of the Sine and Cosine Functions, 8.1 Graphs of the Sine and Cosine Functions, 8.1 Graphs of the Sine and Cosine Functions
sinusoidal function 8.1 Graphs of the Sine and Cosine Functions
slope 2.2 Linear Equations in One Variable, 4.1 Linear Functions
slope-intercept form 4.1 Linear Functions, 4.1 Linear Functions, 4.1 Linear Functions
smooth curve 5.2 Power Functions and Polynomial Functions
solution set 2.2 Linear Equations in One Variable, 11.2 Systems of Linear Equations: Three Variables
solving systems of linear equations 11.1 Systems of Linear Equations: Two Variables
special angles 9.2 Sum and Difference Identities
square matrix 11.5 Matrices and Matrix Operations, 11.8 Solving Systems with Cramer's Rule
square root property 2.5 Quadratic Equations
SSA (side-side-angle) 10.1 Non-right Triangles: Law of Sines
SSS (side-side-side) triangle 10.2 Non-right Triangles: Law of Cosines
standard form 2.2 Linear Equations in One Variable
standard form of a quadratic function 5.1 Quadratic Functions
standard position 7.1 Angles, 7.1 Angles, 10.8 Vectors
stretch 6.2 Graphs of Exponential Functions
stretching/compressing factor 8.2 Graphs of the Other Trigonometric Functions, 8.2 Graphs of the Other Trigonometric Functions
substitution method 11.1 Systems of Linear Equations: Two Variables
sum and difference formulas for cosine 9.2 Sum and Difference Identities
sum and difference formulas for sine 9.2 Sum and Difference Identities
sum and difference formulas for tangent 9.2 Sum and Difference Identities
sum-to-product formulas 9.4 Sum-to-Product and Product-to-Sum Formulas, 9.4 Sum-to-Product and Product-to-Sum Formulas
summation notation 13.4 Series and Their Notations
surface area 5.7 Inverses and Radical Functions
symmetry test 10.4 Polar Coordinates: Graphs
synthetic division 5.4 Dividing Polynomials, 5.5 Zeros of Polynomial Functions
system of equations 11.6 Solving Systems with Gaussian Elimination, 11.6 Solving Systems with Gaussian Elimination, 11.6 Solving Systems with Gaussian Elimination, 11.6 Solving Systems with Gaussian Elimination, 11.7 Solving Systems with Inverses
system of linear equations 4.2 Modeling with Linear Functions, 11.1 Systems of Linear Equations: Two Variables, 11.1 Systems of Linear Equations: Two Variables, 11.1 Systems of Linear Equations: Two Variables
system of nonlinear equations 11.3 Systems of Nonlinear Equations and Inequalities: Two Variables
system of nonlinear inequalities 11.3 Systems of Nonlinear Equations and Inequalities: Two Variables
system of three equations in three variables 11.8 Solving Systems with Cramer's Rule
T
tangent 7.4 The Other Trigonometric Functions, 8.2 Graphs of the Other Trigonometric Functions, 8.2 Graphs of the Other Trigonometric Functions
tangent function 8.2 Graphs of the Other Trigonometric Functions, 8.2 Graphs of the Other Trigonometric Functions, 8.2 Graphs of the Other Trigonometric Functions, 8.2 Graphs of the Other Trigonometric Functions, 9.1 Verifying Trigonometric Identities and Using Trigonometric Identities to Simplify Trigonometric Expressions
term 13.1 Sequences and Their Notations, 13.2 Arithmetic Sequences
term of a polynomial 1.4 Polynomials, 1.4 Polynomials
term of a polynomial function 5.2 Power Functions and Polynomial Functions
terminal point 10.8 Vectors, 10.8 Vectors
terminal side 7.1 Angles
transformation 3.5 Transformation of Functions, 4.1 Linear Functions
translation 12.1 The Ellipse
transverse axis 12.2 The Hyperbola
trigonometric equations 10.6 Parametric Equations
trigonometric functions 7.4 The Other Trigonometric Functions
trigonometric identities 10.2 Non-right Triangles: Law of Cosines
trinomial 1.4 Polynomials
turning point 5.2 Power Functions and Polynomial Functions, 5.3 Graphs of Polynomial Functions
U
union of two events 13.7 Probability
unit circle 7.1 Angles, 7.2 Right Triangle Trigonometry, 7.3 Unit Circle, 7.3 Unit Circle, 9.5 Solving Trigonometric Equations
unit vector 10.8 Vectors
upper limit of summation 13.4 Series and Their Notations
upper triangular form 11.2 Systems of Linear Equations: Three Variables
V
variable 1.1 Real Numbers: Algebra Essentials
varies directly 5.8 Modeling Using Variation, 5.8 Modeling Using Variation
varies inversely 5.8 Modeling Using Variation
vector 10.8 Vectors
vector addition 10.8 Vectors
vertex 5.1 Quadratic Functions, 7.1 Angles, 12.1 The Ellipse, 12.1 The Ellipse, 12.3 The Parabola, 12.3 The Parabola
vertex form of a quadratic function 5.1 Quadratic Functions
vertical asymptote 5.6 Rational Functions, 5.6 Rational Functions, 5.6 Rational Functions, 8.3 Inverse Trigonometric Functions
vertical compression 3.5 Transformation of Functions
vertical line 2.2 Linear Equations in One Variable, 4.1 Linear Functions, 4.1 Linear Functions
vertical line test 3.1 Functions and Function Notation
vertical reflection 3.5 Transformation of Functions
vertical shift 3.5 Transformation of Functions, 4.1 Linear Functions, 6.2 Graphs of Exponential Functions, 6.4 Graphs of Logarithmic Functions, 6.7 Exponential and Logarithmic Models, 8.1 Graphs of the Sine and Cosine Functions
vertical stretch 3.5 Transformation of Functions, 4.1 Linear Functions, 6.4 Graphs of Logarithmic Functions
vertices 12.1 The Ellipse, 12.1 The Ellipse
volume 2.3 Models and Applications
volume of a sphere 5.2 Power Functions and Polynomial Functions
W
whole numbers 1.1 Real Numbers: Algebra Essentials, 1.1 Real Numbers: Algebra Essentials
X
x-axis 2.1 The Rectangular Coordinate Systems and Graphs
x-coordinate 2.1 The Rectangular Coordinate Systems and Graphs
x-intercept 2.1 The Rectangular Coordinate Systems and Graphs, 4.1 Linear Functions
Y
y-axis 2.1 The Rectangular Coordinate Systems and Graphs
y-coordinate 2.1 The Rectangular Coordinate Systems and Graphs
y-intercept 2.1 The Rectangular Coordinate Systems and Graphs, 4.1 Linear Functions
Z
zero-product property 2.5 Quadratic Equations
zeros 5.1 Quadratic Functions, 5.3 Graphs of Polynomial Functions, 5.3 Graphs of Polynomial Functions, 5.5 Zeros of Polynomial Functions, 10.4 Polar Coordinates: Graphs
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