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The Essential Guide to Precalculus
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±âÁ¸¿¡ ÃâÆÇÇÑ ±³°ú´ëºñ ±³ÀçÀÇ Á¤Á¡À» Âï´Â Precalculus ±³À縦 ÃâÆÇÇϸç, ±â´ë°¡ ¸Å¿ì Å®´Ï´Ù. ÀÌ¹Ì À¯¼öÀÇ ´ëÇб³¿¡ ÀÔÇÐÇÑ Á¦Àڵ鿡°Ô ¿©·¯ Â÷·Ê È®ÀÎ ¹× °Ë¼ö¸¦ ¹ÞÀ¸¸é¼ µé¾ú´ø ¿¬±¸¿øµéÀÇ Çǵå¹é Áß º»ÀÎÀÌ ¡°10Çг⠶§ ÀÌ ±³Àç°¡ ÀÖ¾úÀ¸¸é ÁÁ¾Ò¾ú°Ú´Ù¡±¶ó´Â ³»¿ë°ú ¡°°³³äÀ» ±íÀÌ »ý°¢ÇÏ°í, Àû¿ëÇØ¾ß Ç®¸®´Â ¹®Á¦µé À§ÁÖ·Î ÀÛ¼ºµÇ¾ú´Ù¡±¶ó´Â ³»¿ëÀÌ °¡Àå ÀλóÀûÀ̾ú½À´Ï´Ù.
óÀ½À¸·Î Precalculus¸¦ ¹è¿ì´Â ÇлýµéºÎÅÍ, »óÀ§±Ç Çлýµé±îÁö ´Ù ¾Æ¿ì¸¦ ¼ö ÀÖ ´Â ³»¿ë»Ó¸¸ ¾Æ´Ï¶ó, À§ °³³äÀÌ ´©±¸¿¡ ÀÇÇؼ ¾î¶»°Ô ¹ßÀüµÇ¾ú´ÂÁö, ¾î¶»°Ô ¿ì¸® »çȸ¿¡ ¿µÇâÀ» ÁÖ¾ú´ÂÁö±îÁö ¿ª»çÀû °üÁ¡¿¡¼µµ ¼¼úÇÏ¿´´Âµ¥, ÀÌ ºÎºÐÀÌ ½ÇÁ¦·Î ¼ö¾÷À» ÇÏ´Â Çлýµé¿¡°Ô È¿°ú°¡ ¸Å¿ì ÄǽÀ´Ï´Ù. ÀÌ·Î ÀÎÇØ, ¾ÕÀ¸·Î ±³ÀçÀÇ ¹æÇâÀ» ÀâÀ¸¸é¼ ±³Àç ÀÛ¾÷À» ÇØ¿Â ÅͶó, À̹ø ±³Àç ÃâÆÇÀº Á¦°Ô Å« Àǹ̰¡ ÀÖ½À´Ï´Ù.
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Preface .............................................................................................. 3
ÀúÀÚ ¼Ò°³ .............................................................................................. 4
ÀÌ Ã¥ÀÇ Æ¯Â¡ ......................................................................................... 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
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