"기존에 출판한 교과대비 교재의 정점을 찍는 Precalculus 교재를 출판하며, 기대가 매우 큽니다. 이미 유수의 대학교에 입학한 제자들에게 여러 차례 확인 및 검수를 받으면서 들었던 연구원들의 피드백 중 본인이 “10학년 때 이 교재가 있었으면 좋았었겠다”라는 내용과 “개념을 깊이 생각하고, 적용해야 풀리는 문제들 위주로 작성되었다”라는 내용이 가장 인상적이었습니다.

처음으로 Precalculus를 배우는 학생들부터, 상위권 학생들까지 다 아우를 수 있 는 내용뿐만 아니라, 위 개념이 누구에 의해서 어떻게 발전되었는지, 어떻게 우리 사회에 영향을 주었는지까지 역사적 관점에서도 서술하였는데, 이 부분이 실제로 수업을 하는 학생들에게 효과가 매우 컸습니다. 이로 인해, 앞으로 교재의 방향을 잡으면서 교재 작업을 해온 터라, 이번 교재 출판은 제게 큰 의미가 있습니다."

― 저자의 말 중에서

Preface .............................................................................................. 3

저자 소개 .............................................................................................. 4

이 책의 특징 ......................................................................................... 5

TOPIC 1 Essence of Graphs

1.1 | Graphs in Cartesian Coordinates....................................................................................10

1.2 | Distance formula and Midpoint formula........................................................................11

1.3 | Symmetry........................................................................................................................12

1.4 | Application of Analytic Geometry:Circles and Quadratic Curves..................................16

TOPIC 2 Essence of Functions

2.1 | Function Basics................................................................................................................30

2.2 | Function Arithmetic.........................................................................................................32

2.3 | Domain and Range..........................................................................................................35

2.4 | Composition of Functions...............................................................................................80

2.5 | Inverse Function..............................................................................................................83

TOPIC 3 Revisiting Logs and Exponentials

3.1 | Exponential and Logarithmic Functions.........................................................................90

3.2 | Exponential and Logarithmic Property...........................................................................95

TOPIC 4 Trigonometric Ratio

4.1 | Basic Ratio.......................................................................................................................108

4.2 | Extension of Basic Ratio..................................................................................................110

TOPIC 5 Trigonometric Functions

5.1 | Graphs of Primary Trigonometric Functions..................................................................122

5.2 | Transformation of Sinusoidal Functions.........................................................................130

5.3 | Graphs of Reciprocal Trigonometric Functions..............................................................132

5.4 | Maximum and minimum of Trigonometric Functions....................................................137

5.5 | Solving Trigonometric Equations....................................................................................139

5.6 | Inverse Trigonometric Functions....................................................................................146

TOPIC 6 Trigonometric Identities

6.1 | Sum and Difference Formula..........................................................................................156

6.2 | Double-Angle and Half-Angle Formula..........................................................................159

6.3 | Product-to-Sum Formula and Vice Versa........................................................................161

TOPIC 7 Application of Trigonometry

7.1 | Law of Sines and Law of Cosines....................................................................................174

7.2 | Vectors in the Plane.........................................................................................................181

7.3 | Dot Product or Scalar Product........................................................................................183

7.4 | Vector Algebra.................................................................................................................186

7.5 | Complex Numbers...........................................................................................................190

7.6 | Fundamental Theorem of Algebra..................................................................................193

7.7 | Complex Numbers in Polar Form...................................................................................195

7.8 | Multiplication and Division of Complex Numbers in Polar Form.................................197

7.9 | De Moivre's Theorem......................................................................................................198

TOPIC 8 Polar Coordinates and Graphs

8.1 | Polar Coordinates............................................................................................................210

8.2 | Rectangular Coordinates and Polar Coordinates............................................................212

8.3 | Transforming Equations..................................................................................................215

8.4 | Polar Equation of a Line..................................................................................................216

8.5 | Polar Equation of a Circle...............................................................................................219

8.6 | Polar Expressions for Other Conic Sections...................................................................221

8.7 | Cardioid, Limacon, Rose and Lemniscate.......................................................................225

TOPIC 9 Matrices

9.1 | Multiplication Methods for 3×3 Matrices........................................................................240

9.2 | Inverse Matrices for 3×3 Matrices...................................................................................243

9.3 | Elementary Matrices........................................................................................................247

9.4 | Snapshot of Eigenvalue...................................................................................................253

Solution Manual