9780534948542

Analytic Geometry

by
  • ISBN13:

    9780534948542

  • ISBN10:

    0534948545

  • Edition: 6th
  • Format: Hardcover
  • Copyright: 1995-10-25
  • Publisher: Cengage Learning

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Supplemental Materials

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Summary

This respected text makes extensive use of applications and features items such as historical vignettes to make the material useful and interesting. The text is written for the one-term analytic geometry course, often taught in sequence with college algebra, and is designed for students with a reasonably sound background in algebra, geometry, and trigonometry.

Table of Contents

Preface v
Inroduction to the Graphing Calculator ix
Plane Analytic Geometry
1(50)
The Cartesian Plane
1(2)
Distance Formula
3(8)
Point-of-Division Formulas
11(9)
Inclination and Slope
20(5)
Parallel and Perpendicular Lines
25(5)
Angle from One Line to Another
30(6)
Graphs and Points of Intersection
36(9)
An Equation of a Locus
45(6)
Vectors in the Plane
51(34)
Directed Line Segments and Vectors
51(10)
The Dot Product
61(9)
Applications of Vectors
70(15)
The Line
85(41)
Point-Slope and Two-Point Forms
85(11)
Slope-Intercept and Intercept Forms
96(10)
Distance from a Point to a Line
106(9)
Families of Lines
115(11)
The Circle
126(23)
The Standard Form for an Equation of a Circle
126(12)
Conditions to Determine a Circle
138(11)
Conic Sections
149(37)
Inroduction
149(1)
The Parabola
149(12)
The Ellipse
161(12)
The Hyperbola
173(13)
Transformation of Coordinates
186(37)
Translation of Conic Sections
186(14)
Translation of General Equations
200(6)
Rotation
206(5)
The General Equation of Second Degree
211(12)
Curve Sketching
223(58)
Symmetry and Intercepts
223(11)
Sketching Polynomial Equations
234(13)
Asymptotes
247(9)
Sketching Rational Functions
256(9)
Radicals and the Domain of the Equation
265(9)
Direct Sketching of Conics
274(7)
Polar Coordinates and Parametric Equations
281(35)
Polar Coordinates
281(1)
Graphs in Polar Coordinates
282(8)
Points of Intersection
290(4)
Relationships between Rectangular and Polar Coordinates
294(5)
Conics in Polar Coordinates
299(6)
Parametric Equations
305(11)
Solid Analytic Geometry
316(88)
Inroduction: The Distance and Point-of-Division Formulas
316(6)
Vectors in Space
322(6)
Direction Angles, Cosines, and Numbers
328(6)
The Line
334(8)
The Cross Product
342(9)
The Plane
351(10)
Cylinders and Spheres
361(4)
Quadric Surfaces
365(13)
Cylindrical and Spherical Coordinates
378(9)
APPENDICES
A Trigonometry Review
387(8)
B Formulas
395(4)
C Theorems from Plane Geometry
399(5)
Answers to Odd-Numbered Problems 404(65)
Index 469

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