# The mainstream of algebra and trigonometry

Houghton Mifflin, Jan 1, 1980 - Mathematics - 506 pages

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### Contents

 Real Numbers and Algebraic Expressions 2 Coordinate Lines and Absolute Values 12 Integral Exponents 18 Radicals 24 Rational Exponents and Scientific Notation 29 Polynomials and Algebraic Expressions 36 Factoring Polynomials 42 Rational Expressions 47
 The Law of Cosines 290 The Law of Sines 295 Review 304 Trigonometric Identities Equations and Inverse Functions Vectors 307 Trigonometric Identities 308 More Trigonometric Identities 312 Trigonometric Equations 316 The Addition Formulas for the Cosine 319

 Review 53 Equations and Inequalities in One Variable 58 Applications to Word Problems 64 Quadratic Equations 74 More Equations 82 Linear Inequalities 87 Quadratic and Other Inequalities 94 Equations and Inequalities Involving Absolute Values 98 Review 101 Functions and Graphs 106 Graphs of Equations 112 Functions 121 Graphs of Functions 127 Lines and Linear Functions 135 Composite and Inverse Functions 144 Variation 152 Review 156 Systematic Graphing 162 Polynomial Functions 171 Rational Functions 175 Conic Sections 185 Review 196 Exponential and Logarithmic Functions 200 Logarithmic Functions 209 Common and Natural Logarithms 219 Exponential and Logarithmic Equations 226 Linear Interpolation 231 Review 234 The Trigonometric Functions 238 Applications 249 Angles 257 The Trigonometric Functions 265 Graphs of the Trigonometric Functions 277 Periodic Functions 282
 The Addition Formulas for the Sine and Tangent 326 The MultipleAngle Formulas 330 Product to Sum Sum to Product Formulas 336 The Inverse Trigonometric Functions 340 Vectors 347 Force and Velocity Applications 352 Review 357 Systems of Equations and Inequalities 362 More Systems of Equations in Two Variables 370 Systems of Linear Equations in Three or More Variables 373 Matrices 378 Determinants and Cramers Rule 382 Systems of Inequalities and Linear Programming 388 Review 397 Complex Numbers 402 Geometric Representation of Complex Numbers 409 Polar Form for Complex Numbers 411 De Moivres Theorem 415 Review 418 Polynomials 422 A Computation Method for Polynomials 423 The Remainder Theorem 426 Synthetic Division 432 Polynomials with Real Coefficients 436 Rational Zeros of Polynomials 438 Review 442 Induction Sequences and the Binomial Theorem 446 Summation Notation 451 Sequences 455 The Binomial Theorem 460 Review 469 Table A Squares and Square Roots 1200 471 Index 501 Copyright