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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.

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