College Algebra and Trigonometry

	*Interactive Educational Software for e-Learning Math!*

	Home Products & Demos Ordering System Requirements Testimonials Install/Uninstall Contact Us

College Algebra and Trigonometry release 25.63

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
Linear and Absolute Value Functions
- Linear Equations and Inequalities in One Variable
  - Solving Linear Equations
  - Solving Linear Inequalities
  - Solving Equations Involving Absolute Values
  - Solving Inequalities Involving Absolute Values
- 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
- Equations of Straight Lines
  - Slope of a Line
  - Slope-Intercept Equation of a Line
  - Point-Slope Equation of a Line
  - Slopes for Parallel Lines
  - Slopes for Perpendicular Lines
Systems of Linear Equations and Inequalities
- Systems of Two Linear Equations in Two Variables
  - Basic Concepts
  - Solutions Using Graphing
  - Solutions Using Substitution
  - Solutions Using Elimination
- Linear Inequalities in Two Variables
- Systems of Linear Inequalities in Two Variables
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
- The Scalar Product
- Matrix Addition
- Matrix Multiplication
- Inverses of Matrices
- Systems of Equations: Use of Matrix Inverses
Polynomial and Rational Functions
- Division of Polynomials
- Roots of Polynomial Equations
  - The Factor Theorem
  - Rational Zeros
  - The Remainder Theorem
  - Descartes' Rule of Signs
- Graphing Rational Functions
  - Vertical Asymptotes for the Graph of Rational Functions
  - Horizontal Asymptotes for the Graph of Rational Functions
  - Oblique Asymptotes for the Graph of Rational Functions
Complex Numbers
- Basic Definitions and Graphical Representation of Complex Numbers
- Operations with Complex Numbers
  - Conjugate Complex Numbers
  - Addition
  - Subtraction
  - Multiplication
  - Division
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
  - Complex Roots of a Quadratic Equation
  - The Sum and the Product of the Roots
- Graphic Solution of Quadratic Inequalities
Conic Sections
- The Parabola
- The Ellipse
- The Hyperbola
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
  - Exponential Growth or Decay
Angles and their Measure
- Basic Definitions
- Converting between Degrees and Radians
- Arc Length
- Area of a Sector
Trigonometric Functions
- Directed Length of Arc
- 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=A*sin(bx+c)
- Transformations of the Cosine Graph
  - Phase Shift
  - Amplitude
  - Period
  - Graph of y=A*cos(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 Equations
Vectors in the Plane
- Basic Definitions
- The Algebra of Vectors
  - Multiplication by Scalars
  - Addition
  - Subtraction
  - Computations with Vectors
- The Scalar Product
  - Basic Definitions
  - Computations with Scalar Product
Polar Coordinate System
- Polar Coordinates
- Conversion from Polar to Rectangular Coordinates
- Conversion from Rectangular to Polar Coordinates
- Graphing Polar Equations
  - Cardioid
  - Four-leaved Rose
  - Limacon
  - Spiral of Archimedes
Operations with Complex Numbers in Polar Form
- Polar Form of a Complex Number
- Multiplication of Complex Numbers in Polar Form
- Division of Complex Numbers in Polar Form
- Powers of Complex Numbers. DeMoivre's Theorem
- Roots of Complex Numbers
Sequences and Series
- Arithmetic Sequences
- Arithmetic Series
- Geometric Sequences
- Geometric Series
- Infinite Geometric Series
Miscellaneous
- Binomial Theorem
  - Factorial Notation
  - Binomial Expansions
  - Pascal's Triangle
- Counting Principles
  - Permutations
    - Permutations of n Elements
    - Permutations of n Elements Taken r at a Time
    - Distinguishable Permutations
  - Combinations
  - Fundamental Counting Principles