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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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