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Precalculus
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Precalculus
release 15.33
FULL VERSION
Contents
Rectangular Coordinate System
Rectangular Coordinates of a Point
The Distance Formula
Circles
The Midpoint Formula
Functions and Graphs
Basic Definitions and Notations
Graphs of Functions
Composite Functions
Inverse Functions
Transformations of Graphs
Translating Graphs of Functions
Stretching and Compressing Graphs of Functions
Combining Transformations
Graphic Solution of Equations
Graphic Solution of Inequalities
Linear and Absolute Value Functions
Solving Linear Equations
Solving Linear Inequalities
Equations of Straight Lines
Graphs and Graphic Solutions
Graph of the Function y=ax + b
Graph of the Function y=|ax+b|
Graphic Solution of the Equation |ax + b| = c
Graphic Solution of the Inequality |ax + b| <> c
Slope of a Line
Point-Slope Equation of a Line
Slope-Intercept Equation of a Line
Slopes for Parallel Lines
Slopes for Perpendicular Lines
Solving Equations Involving Absolute Values
Solving Inequalities Involving Absolute Values
Systems of Linear Inequalities
Graphic Solution of a System of Two Linear Inequalities in Two Variables
Graphic Solution of a System of Three Linear Inequalities
Quadratic Functions
Completing the Square
Factoring Trinomials by Completing the Square
Graphs of Quadratic Functions
Maximum and Minimum Problems
Solving Quadratic Equations
Solving Quadratic Equations by Completing the Square
Solving Quadratic Equations by General Formula
The Sum and the Product of the Roots
Graphic Solution of Quadratic Inequalities
Polynomial and Rational Functions
Operations with Polynomials
Addition of Polynomials
Subtraction of Polynomials
Multiplication of Polynomials
Division of Polynomials
The Remainder Theorem
The Factor Theorem
Descartes' Rule of Signs
Rational Zeros
Asymptotes
Vertical Asymptotes for the Graph of Rational Functions
Horizontal Asymptotes for the Graph of Rational Functions
Oblique Asymptotes for the Graph of Rational Functions
Exponential and Logarithmic Functions
Graphs of Functions
Exponential Function
Logarithmic Function
Exponential and Logarithmic Functions
Properties of Logarithms
Solving Exponential and Logarithmic Equations
Solving Exponential Equations
Solving Logarithmic Equations
Applications
Compound Interest
Growth and Decay
Angles and their Measure
Basic Definitions
Converting between Degrees and Radians
Arc Length
Area of a Sector
Trigonometric Functions
The Sine Function
The Cosine Function
The Tangent Function
The Cotangent Function
The Secant Function
The Cosecant Function
Trigonometric Identities
Basic Identities
Multiple-Angle Identities
Sum and Difference Identities
Transformations of Trigonometric Graphs
Transformations of the Sine Graph
Phase Shift
Amplitude
Period
Graph of y=Asin(bx+c)
Transformations of the Cosine Graph
Phase Shift
Amplitude
Period
Graph of y=Acos(bx+c)
Transformations of the Tangent Graph
Phase Shift
Period
Graph of y=Atan(bx+c)
Transformations of the Cotangent Graph
Phase Shift
Period
Graph of y=Acot(bx+c)
Inverse Trigonometric Functions
The Inverse Sine Function
The Inverse Cosine Function
The Inverse Tangent Function
The Inverse Cotangent Function
Computations with Inverse Trigonometric Functions
Solving Triangles
Solving Right Triangles
One Side and One Angle are Given
Two Sides are Given
The Law of Cosines
The Law of Sines
Trigonometric Equations
Simple Trigonometric Equations
Solving Equation sinx = c
Solving Equation cosx = c
Solving Equation tanx=c
Solving Equation cotx = c
Equations Reducible to Simple Equation
Polar Coordinate System
Polar Coordinates
Conversion from Polar to Rectangular Coordinates
Conversion from Rectangular to Polar Coordinates
Graphs of a Polar Equations
Cardioid
Four-leaved Rose
Limacon
Spiral of Archimedes
Vectors in the Plane
Basic Definitions
The Algebra of Vectors
Addition
Subtraction
Multiplication by Scalars
Computations with Vectors
The Scalar Product
Basic Definitions
Computations with Scalar Product
Complex Numbers
Basic Definitions and Graphical Representation of Complex Numbers
Operations with Complex Numbers
Conjugate Complex Numbers
Addition
Subtraction
Multiplication
Division
Complex Roots of a Quadratic Equation
Polar Form of a Complex Number
Division of Complex Numbers in the Polar Form
Multiplication of Complex Numbers in the Polar Form
Second Degree Equations
The Parabola
The Ellipse
The Hyperbola
Determinants and Cramer's Rule
Determinants of Order 2
Determinants of Order 3
Definition and Properties of Determinants
Minors and Cofactors
The Expansion Theorem
Systems of Two Linear Equations in Two Unknowns. Cramer's Rule
Systems of Three Linear Equations in Three Unknowns. Cramer's Rule
Matrices
Basic Definitions
Matrix Addition
The Scalar Product
Matrix Multiplication
Inverses of Matrices
Systems of Equations: Use of Matrix Inverses
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