Trigonometry for dummies:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Indianapolis, Ind.
Wiley
c2005
|
| Schriftenreihe: | --For dummies
|
| Schlagworte: | |
| Online-Zugang: | Contributor biographical information Publisher description Table of contents only Inhaltsverzeichnis |
| Beschreibung: | Includes index |
| Beschreibung: | XVI, 368 S. Ill., graph. Darst. 24 cm |
| ISBN: | 0764569031 |
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Datensatz im Suchindex
| _version_ | 1804136312734744576 |
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| adam_text | TRIGONOMETRY FOR BY MARY JANE STERLING SUB GOTTINGEN 7 217 806 120 2005
A 5579 WILEY WILEY PUBLISHING, INC. TABLE OF CONTENTS INTRODUCTION /
ABOUT THIS BOOK 1 CONVENTIONS USED IN THIS BOOK 2 FOOLISH ASSUMPTIONS 2
WHAT YOU RE NOT TO READ 3 HOW THIS BOOK IS ORGANIZED 3 PART I: THE
BASICS 3 PART II: TRIGONOMETRIC FUNCTIONS 3 PART III: IDENTITIES 4 PART
IV: EQUATIONS AND APPLICATIONS 4 PART V: GRAPHS OF TRIG FUNCTIONS 4 PART
VI: THE PART OF TENS 4 ICONS USED IN THIS BOOK 4 WHERE TO GO FROM HERE 5
PART 1: THE BASICS 7 CHAPTER 1: TROUNCING TRIG TECHNICALITIES 9 TAKING
TRIG FOR A RIDE: WHAT TRIG IS 9 SIZING UP THE BASIC FIGURES 9 ANGLING
FOR POSITION 11 TRIANGULATING YOUR POSITION 13 CIRCLING THE WAGONS :. 14
UNDERSTANDING TRIG SPEAK :. 18 DEFINING TRIG FUNCTIONS 19 TAMING THE
RADICALS 21 EQUATING AND IDENTIFYING 23 GRAPHING FOR GOLD 25 DESCRIBING
GRAPHING SCALES 25 RECOGNIZING BASIC GRAPHS 25 CHAPTER 2: COORDINATING
YOUR EFFORTS WITH CARTESIAN COORDINATES 29 STARTING OUT SIMPLE: PLOTTING
POINTS 29 AXES, AXES, WE ALL FALL DOWN 30 DETERMINING THE ORIGIN OF IT
ALL 30 PLOTTING X VERSUS Y 31 CUTTING THE GRAPH INTO FOUR PARTS 31
TRIGONOMETRY FOR DUMMIES FROM HERE TO THERE: CALCULATING DISTANCES 33
COUNTING ON VERTICAL AND HORIZONTAL DISTANCES 33 ANOTHER SLANT: DIAGONAL
DISTANCES 34 USING EXACT VALUES OR ESTIMATING DISTANCES 36 GETTING TO
THE CENTER OF IT ALL 36 FINDING THE MIDPOINT OF A LINE SEGMENT 37
LOCATING THE CENTER OF A CIRCLE 37 PARTITIONING LINE SEGMENTS FURTHER 39
PINPOINTING THE CENTER OF A TRIANGLE 41 RACING DOWN THE SLOPE 43
SLALOMING SLOPE FORMULA 43 RECOGNIZING PARALLEL AND PERPENDICULAR LINES
44 DEFINING CIRCLES WITH NUMBERS 45 CENTERING CIRCLES AT THE ORIGIN 45
WANDERING CENTERS 46 CHAPTER 3: FUNCTIONING WELL 47 RELATIONS VERSUS
FUNCTIONS 47 FUNCTION JUNCTION, WHAT S YOUR FUNCTION? 48 USING FUNCTION
NOTATION 48 DETERMINING DOMAIN AND RANGE 49 IN-VERSE FUNCTIONS: RHYME OR
REASON? 50 WHICH FUNCTIONS HAVE INVERSES? 50 FINDING AN INVERSE FUNCTION
52 TRANSFORMING FUNCTIONS 53 TRANSLATING A FUNCTION 53 REFLECTING LIKE A
MIRROR 55 CHAPTER 4: GETTING YOUR DEGREE 57 ANGLES, ANGLES EVERYWHERE:
MEASURING IN DEGREES 57 SLICING A COORDINATE PLANE 58 LOOKING ELSEWHERE
FOR DEGREE MEASURES 59 GRAPHING ANGLES IN STANDARD POSITION 62
POSITIONING INITIAL AND TERMINAL SIDES 62 MEASURING BY QUADRANTS 62
WHAT S YOUR ANGLE? LABELING IN VARIOUS WAYS 64 USING NEGATIVE ANGLE
MEASURES :....64 CO-MINGLING WITH COTERMINAL ANGLES 65 RENAMING ANGLES:
SO MANY ALIASES 66 CHAPTER 5: DISHING OUT THE PI: RADIANS 69 WHAT S IN A
RADIAN? 69 RELATING TO A CIRCLE 70 CONVERTING DEGREES AND RADIANS 70
HIGHLIGHTING FAVORITES 74 TABLE OF CONTENTS MAKING A CLONE OF ARC 74
TAKING CHUNKS OUT OF CIRCLES 75 SWEEPING HANDS :...78 GOING OUT AND
ABOUT 79 CHAPTER 6: GETTING IT RIGHT WITH TRIANGLES 83 SIZING UP RIGHT
TRIANGLES 83 WHAT S SO RIGHT ABOUT THEM? 83 THE ANATOMY OF A RIGHT
TRIANGLE 84 PYTHAGORAS SCHMYTHAGORAS: DEMYSTIFYING THE PYTHAGOREAN
THEOREM 86 HITTING A PYTHAGOREAN TRIPLE 87 SOLVING FOR A MISSING LENGTH
88 IN A LEAGUE OF THEIR OWN: SPECIAL RIGHT TRIANGLES 91 30-60-90 RIGHT
TRIANGLES 91 ISOSCELES RIGHT TRIANGLES 92 PART 11: TRIGONOMETRIC
FUNCTIONS 93 CHAPTER 7: DOING RIGHT BY TRIG FUNCTIONS 95 SOHCAHTOA TO
THE RESCUE: HOW TRIG FUNCTIONS WORK 95 THE NAME GAME: A RIGHT TRIANGLE S
THREE SIDES 96 THE SIX RATIOS: RELATING THE THREE SIDES 96 THE SINE
FUNCTION: OPPOSITE OVER HYPOTENUSE 97 THE COSINE FUNCTION: ADJACENT OVER
HYPOTENUSE 98 THE TANGENT FUNCTION: OPPOSITE OVER ADJACENT 99 ALL
TOGETHER, NOW: USING ONE FUNCTION TO SOLVE FOR ANOTHER 100 SOCKING THE
RULES AWAY: THE LEGEND OF SOHCAHTOA 101 TAKING IT A STEP FURTHER:
RECIPROCAL FUNCTIONS I- 101 THE COSECANT FUNCTION: SINE FLIPPED UPSIDE
DOWN 102 THE SECANT FUNCTION: COSINE ON ITS HEAD 103 THE COTANGENT
FUNCTION: TANGENT, TAILS SIDE UP 103 ANGLING IN ON YOUR FAVORITES 105
IDENTIFYING THE MOST POPULAR ANGLES 105 DETERMINING THE EXACT VALUES OF
FUNCTIONS 106 CHAPTER 8: TRADING TRIANGLES FOR CIRCLES: CIRCULAR
FUNCTIONS ILL GETTING ACQUAINTED WITH THE UNIT CIRCLE ILL PLACING POINTS
ON THE UNIT CIRCLE 112 FINDING A MISSING COORDINATE 114 GOING FULL
CIRCLE WITH THE ANGLES 116 STAYING POSITIVE 116 BEING NEGATIVE OR
MULTIPLYING YOUR ANGLES 116 LOCATING AND COMPUTING REFERENCE ANGLES 117
XII TRIGONOMETRY FOR DUMMIES DEFINING TRIG FUNCTIONS FOR ALL ANGLES 121
PUTTING REFERENCE ANGLES TO USE 122 LABELING THE OPTIMISTS AND
PESSIMISTS .122 COMBINING ALL THE RULES 123 USING COORDINATES OF CIRCLES
TO SOLVE FOR TRIG FUNCTIONS 125 CALCULATING WITH COORDINATES ON THE UNIT
CIRCLE 127 CALCULATING WITH COORDINATES ON ANY CIRCLE AT THE ORIGIN 128
DEFINING DOMAINS AND RANGES OF TRIG FUNCTIONS 130 FRIENDLY FUNCTIONS:
SINE AND COSINE 131 CLOSE COUSINS OF THEIR RECIPROCALS: COSECANT AND
SECANT 132 BROTHERS OUT ON THEIR OWN: TANGENT AND COTANGENT 133 CHAPTER
9: APPLYING YOURSELF TO TRIG FUNCTIONS 135 FIRST THINGS FIRST: ELEVATING
AND DEPRESSING 135 ANGLE OF ELEVATION 136 ANGLE OF DEPRESSION 137
MEASURING TALL BUILDINGS WITH A SINGLE BOUND 137 RESCUING A DAMSEL FROM
A TOWER 137 DETERMINING THE HEIGHT OF A TREE 139 MEASURING THE DISTANCE
BETWEEN BUILDINGS 140 MEASURING SLOPE 142 THE SKY S (NOT) THE LIMIT 143
SPOTTING A BALLOON 144 TRACKING A ROCKET 146 MEASURING THE VIEW OF
SATELLITE CAMERAS 148 CALCULATING ODD SHAPES AND MANEUVERING CORNERS 149
FINDING THE AREA OF A TRIANGULAR PIECE OF LAND 149 MOVING AN OBJECT
AROUND A CORNER 151 PART 111: IDENTITIES 155 CHAPTER 10: TRIG S BASIC
IDENTITIES 157 FLIPPING FUNCTIONS ON THEIR BACKS: RECIPROCAL IDENTITIES
157 FUNCTION TO FUNCTION: RATIO IDENTITIES 159 OPPOSITES ATTRACT:
OPPOSITE-ANGLE IDENTITIES 159 REVISITING THE CLASSIC THEOREM:
PYTHAGOREAN IDENTITIES 162 THE MOTHER OF ALL PYTHAGOREAN IDENTITIES 163
EXTENDING TO TANGENT AND SECANT 164 FINISHING UP WITH COTANGENT AND
COSECANT 165 REARRANGING THE PYTHAGOREAN IDENTITIES ...165 COMBINING THE
IDENTITIES 167 THE MANY FACES OF SINE 168 WORKING OUT THE VERSIONS 168
TABLE OF CONTENTS CHAPTER 11: OPERATING ON IDENTITIES 171 SUMMING IT UP
,171 OVERCOMING THE DIFFERENCES 175 DOUBLING YOUR MONEY 179 ONE PLUS ONE
EQUALS TWO SINES 179 THREE S A CROWD .180 HALVING FUN YET? 182
EXPLAINING THE 183 HALF A TANGENT IS DOUBLE THE FUN 183 USING
HALF-ANGLE IDENTITIES 184 CHAPTER 12: PROVING IDENTITIES 187 LINING UP
THE PLAYERS 187 PICKING SIDES 189 WORKING ON BOTH SIDES 192 GOING BACK
TO SQUARE ONE 194 CHANGING TO SINES AND COSINES 194 FACTORING 197 USING
A LITTLE BIT OF BOTH 198 FRACTURING FRACTIONS 200 BREAKING UP IS HARD TO
DO 200 FINDING A COMMON DENOMINATOR 202 USING TRICKS OF THE TRIG TRADE
203 MULTIPLYING BY A CONJUGATE 204 SQUARING BOTH SIDES 206 IDENTIFYING
WITH THE OPERATIONS 207 ADDING IT UP 207 WHAT DIFFERENCE DOES IT MAKE?
208 MULTIPLYING YOUR FUN 210 HALVING FUN, WISH YOU WERE HERE 211 PART
IV: EQUATIONS AND APPLICATIONS ..213 CHAPTER 13: INVESTIGATING INVERSE
TRIG FUNCTIONS 215 WRITING IT RIGHT 215 USING THE NOTATION 216
DISTINGUISHING BETWEEN THE FEW AND MANY 217 DETERMINING DOMAIN AND RANGE
OF INVERSE TRIG FUNCTIONS 219 INVERSE SINE FUNCTION 220 INVERSE COSINE
FUNCTION 220 INVERSE TANGENT FUNCTION 220 INVERSE COTANGENT FUNCTION 220
INVERSE SECANT FUNCTION 221 INVERSE COSECANT FUNCTION 221 SUMMARIZING
DOMAIN AND RANGE 221 TRIGONOMETRY FOR DUMMIES WORKING WITH INVERSES 223
GETTING FRIENDLY WITH YOUR CALCULATOR 224 CHANGING THE MODE
.....;....224 INTERPRETING NOTATION ON THE CALCULATOR 225 MULTIPLYING
THE INPUT 227 SOLVING SOME MIXED PROBLEMS 228 CHAPTER 14: SOLVING TRIG
EQUATIONS 231 GENERATING SIMPLE SOLUTIONS 232 FACTORING IN THE SOLUTIONS
233 FINDING A GREATEST COMMON FACTOR 234 FACTORING QUADRATICS... 235
INCREASING THE DEGREES IN FACTORING 237 FACTORING BY GROUPING 239 USING
THE QUADRATIC FORMULA 241 INCORPORATING IDENTITIES 242 FINDING
MULTIPLE-ANGLE SOLUTIONS 245 SQUARING BOTH SIDES 247 MULTIPLYING THROUGH
249 SOLVING WITH A GRAPHING CALCULATOR 249 CHAPTER 15: OBEYING THE LAWS
253 DESCRIBING THE PARTS OF TRIANGLES 253 STANDARDIZING THE PARTS 254
DETERMINING A TRIANGLE 254 FOLLOWING THE LAW OF SINES 256 CONTINUING
WITH THE LAW OF COSINES 260 DEFINING THE LAW OF COSINES 260 LAW OF
COSINES FOR SAS 261 LAW OF COSINES FOR SSS , 263 BEING AMBIGUOUS * 265
INCLUDING THE LAW OF TANGENTS ; 268 FINDING THE AREAS OF TRIANGLES 270
FINDING AREA WITH BASE AND HEIGHT 271 FINDING AREA WITH THREE SIDES 273
FINDING AREA WITH SAS 274 FINDING AREA WITH ASA : 275 PART V: THE GRAPHS
OF TRIG FUNCTIONS. 277 CHAPTER 16: GRAPHING SINE AND COSINE 279 THE ABCS
OF GRAPHING 279 WAVING AT THE SINE 280 DESCRIBING AMPLITUDE AND PERIOD
280 FORMALIZING THE SINE EQUATION 282 TRANSLATING THE SINE 283 TABLE OF
CONTENTS GRAPHING COSINE 285 COMPARING COSINE TO SINE 286 USING
PROPERTIES TO GRAPH COSINE .287 APPLYING THE SINES OF THE TIMES 288
SUNNING YOURSELF 288 AVERAGING TEMPERATURE 290 TAKING YOUR TEMPERATURE
291 MAKING A GOAL 292 THEORIZING WITH BIORHYTHMS 292 CHAPTER 17:
GRAPHING TANGENT AND COTANGENT 295 CHECKING OUT TANGENT 295 DETERMINING
THE PERIOD 296 ASSIGNING THE ASYMPTOTES 296 FIDDLING WITH THE TANGENT V
299 MULTIPLYING THE TANGENT 299 MULTIPLYING THE ANGLE 299 ADDING TO
TANGENT 300 CONFRONTING THE COTANGENT 304 CHAPTER 18: GRAPHING OTHER
TRIG FUNCTIONS 307 SEEING THE COSECANT FOR WHAT IT IS 307 IDENTIFYING
THE ASYMPTOTES 307 USING THE SINE GRAPH 308 VARYING THE COSECANT 310
UNVEILING THE SECANT 312 DETERMINING THE ASYMPTOTES 312 SKETCHING THE
GRAPH OF SECANT 312 FOOLING AROUND WITH SECANT 312 LAYING OUT THE
INVERSE FUNCTIONS 315 GRAPHING INVERSE SINE AND COSINE 316 TAKING ON
INVERSE TANGENT AND COTANGENT 317 CRAFTING INVERSE SECANT AND COSECANT
318 CHAPTER 19: TOPPING OFF TRIG GRAPHS 321 THE BASICS OF TRIG EQUATIONS
321 FLIPPING OVER A HORIZONTAL LINE : 322 INTERPRETING THE EQUATION 323
GRAPHING WITH THE GENERAL FORM 323 ADDING AND SUBTRACTING FUNCTIONS 328
APPLYING YOURSELF TO THE TASK 330 MEASURING THE TIDE 330 TRACKING THE
DEER POPULATION 332 MEASURING THE MOVEMENT OF AN OBJECT ON A SPRING 332
TRIGONOMETRY FOR DUMMIES PART VI: THE PART OF TENS 335 CHAPTER 20: TEN
BASIC IDENTITIES... PLUS ONE 337 RECIPROCAL IDENTITIES 337 RATIO
IDENTITIES 338 PYTHAGOREAN IDENTITIES 338 OPPOSITE-ANGLE IDENTITIES 338
CHAPTER 21: TEN NOT-SO-BASIC IDENTITIES 341 PRODUCT-TO-SUM IDENTITIES
341 SUM-TO-PRODUCT IDENTITIES 342 REDUCTION FORMULA 343 MOLLWEIDE S
EQUATIONS 343 CHAPTER 22: TEN WAYS TO FIND THE AREA OF A TRIANGLE 345
USING THE BASE AND HEIGHT 346 ACQUAINTING YOURSELF WITH HERON 346
APPLYING TRIG (THE WHOLE POINT OF THIS BOOK) 346 ) SIDE-ANGLE-SIDE
FORMULAS. 347 ANGLE-SIDE-ANGLE FORMULAS 347 GOING BACK TO ALGEBRA: USING
DETERMINANTS 347 CHAPTER 23: TEN SINE CURVES REPRESENTING MONTHLY
TEMPERATURES 349 BOSTON, MASSACHUSETTS 349 CHICAGO, ILLINOIS 350 DENVER,
COLORADO 350 FAIRBANKS, ALASKA 350 GALVESTON, TEXAS 350 HONOLULU, HAWAII
:. 350 MIAMI, FLORIDA 351 SAN DIEGO, CALIFORNIA.... 351 SAN JUAN,
PUERTO RICO 351 SAULT STE. MARIE, MICHIGAN 351 APPENDIX: TRIG FUNCTIONS
TABLE 353 INDEX 357
|
| adam_txt |
TRIGONOMETRY FOR BY MARY JANE STERLING SUB GOTTINGEN 7 217 806 120 2005
A 5579 WILEY WILEY PUBLISHING, INC. TABLE OF CONTENTS INTRODUCTION /
ABOUT THIS BOOK 1 CONVENTIONS USED IN THIS BOOK 2 FOOLISH ASSUMPTIONS 2
WHAT YOU'RE NOT TO READ 3 HOW THIS BOOK IS ORGANIZED 3 PART I: THE
BASICS 3 PART II: TRIGONOMETRIC FUNCTIONS 3 PART III: IDENTITIES 4 PART
IV: EQUATIONS AND APPLICATIONS 4 PART V: GRAPHS OF TRIG FUNCTIONS 4 PART
VI: THE PART OF TENS 4 ICONS USED IN THIS BOOK 4 WHERE TO GO FROM HERE 5
PART 1: THE BASICS 7 CHAPTER 1: TROUNCING TRIG TECHNICALITIES 9 TAKING
TRIG FOR A RIDE: WHAT TRIG IS 9 SIZING UP THE BASIC FIGURES 9 ANGLING
FOR POSITION 11 TRIANGULATING YOUR POSITION 13 CIRCLING THE WAGONS :. 14
UNDERSTANDING TRIG SPEAK ':. 18 DEFINING TRIG FUNCTIONS 19 TAMING THE
RADICALS 21 EQUATING AND IDENTIFYING 23 GRAPHING FOR GOLD 25 DESCRIBING
GRAPHING SCALES 25 RECOGNIZING BASIC GRAPHS 25 CHAPTER 2: COORDINATING
YOUR EFFORTS WITH CARTESIAN COORDINATES 29 STARTING OUT SIMPLE: PLOTTING
POINTS 29 AXES, AXES, WE ALL FALL DOWN 30 DETERMINING THE ORIGIN OF IT
ALL 30 PLOTTING X VERSUS Y 31 CUTTING THE GRAPH INTO FOUR PARTS 31
TRIGONOMETRY FOR DUMMIES FROM HERE TO THERE: CALCULATING DISTANCES 33
COUNTING ON VERTICAL AND HORIZONTAL DISTANCES 33 ANOTHER SLANT: DIAGONAL
DISTANCES 34 USING EXACT VALUES OR ESTIMATING DISTANCES 36 GETTING TO
THE CENTER OF IT ALL 36 FINDING THE MIDPOINT OF A LINE SEGMENT 37
LOCATING THE CENTER OF A CIRCLE 37 PARTITIONING LINE SEGMENTS FURTHER 39
PINPOINTING THE CENTER OF A TRIANGLE 41 RACING DOWN THE SLOPE 43
SLALOMING SLOPE FORMULA 43 RECOGNIZING PARALLEL AND PERPENDICULAR LINES
44 DEFINING CIRCLES WITH NUMBERS 45 CENTERING CIRCLES AT THE ORIGIN 45
WANDERING CENTERS 46 CHAPTER 3: FUNCTIONING WELL 47 RELATIONS VERSUS
FUNCTIONS 47 FUNCTION JUNCTION, WHAT'S YOUR FUNCTION? 48 USING FUNCTION
NOTATION 48 DETERMINING DOMAIN AND RANGE 49 IN-VERSE FUNCTIONS: RHYME OR
REASON? 50 WHICH FUNCTIONS HAVE INVERSES? 50 FINDING AN INVERSE FUNCTION
52 TRANSFORMING FUNCTIONS 53 TRANSLATING A FUNCTION 53 REFLECTING LIKE A
MIRROR 55 CHAPTER 4: GETTING YOUR DEGREE 57 ANGLES, ANGLES EVERYWHERE:
MEASURING IN DEGREES 57 SLICING A COORDINATE PLANE 58 LOOKING ELSEWHERE
FOR DEGREE MEASURES 59 GRAPHING ANGLES IN STANDARD POSITION 62
POSITIONING INITIAL AND TERMINAL SIDES 62 MEASURING BY QUADRANTS 62
WHAT'S YOUR ANGLE? LABELING IN VARIOUS WAYS 64 USING NEGATIVE ANGLE
MEASURES :.64 CO-MINGLING WITH COTERMINAL ANGLES 65 RENAMING ANGLES:
SO MANY ALIASES 66 CHAPTER 5: DISHING OUT THE PI: RADIANS 69 WHAT'S IN A
RADIAN? 69 RELATING TO A CIRCLE 70 CONVERTING DEGREES AND RADIANS 70
HIGHLIGHTING FAVORITES 74 TABLE OF CONTENTS MAKING A CLONE OF ARC 74
TAKING CHUNKS OUT OF CIRCLES 75 SWEEPING HANDS :.78 GOING OUT AND
ABOUT 79 CHAPTER 6: GETTING IT RIGHT WITH TRIANGLES 83 SIZING UP RIGHT
TRIANGLES 83 WHAT'S SO RIGHT ABOUT THEM? 83 THE ANATOMY OF A RIGHT
TRIANGLE 84 PYTHAGORAS SCHMYTHAGORAS: DEMYSTIFYING THE PYTHAGOREAN
THEOREM 86 HITTING A PYTHAGOREAN TRIPLE 87 SOLVING FOR A MISSING LENGTH
88 IN A LEAGUE OF THEIR OWN: SPECIAL RIGHT TRIANGLES 91 30-60-90 RIGHT
TRIANGLES 91 ISOSCELES RIGHT TRIANGLES 92 PART 11: TRIGONOMETRIC
FUNCTIONS 93 CHAPTER 7: DOING RIGHT BY TRIG FUNCTIONS 95 SOHCAHTOA TO
THE RESCUE: HOW TRIG FUNCTIONS WORK 95 THE NAME GAME: A RIGHT TRIANGLE'S
THREE SIDES 96 THE SIX RATIOS: RELATING THE THREE SIDES 96 THE SINE
FUNCTION: OPPOSITE OVER HYPOTENUSE 97 THE COSINE FUNCTION: ADJACENT OVER
HYPOTENUSE 98 THE TANGENT FUNCTION: OPPOSITE OVER ADJACENT 99 ALL
TOGETHER, NOW: USING ONE FUNCTION TO SOLVE FOR ANOTHER 100 SOCKING THE
RULES AWAY: THE LEGEND OF SOHCAHTOA 101 TAKING IT A STEP FURTHER:
RECIPROCAL FUNCTIONS I- 101 THE COSECANT FUNCTION: SINE FLIPPED UPSIDE
DOWN 102 THE SECANT FUNCTION: COSINE ON ITS HEAD 103 THE COTANGENT
FUNCTION: TANGENT, TAILS SIDE UP 103 ANGLING IN ON YOUR FAVORITES 105
IDENTIFYING THE MOST POPULAR ANGLES 105 DETERMINING THE EXACT VALUES OF
FUNCTIONS 106 CHAPTER 8: TRADING TRIANGLES FOR CIRCLES: CIRCULAR
FUNCTIONS ILL GETTING ACQUAINTED WITH THE UNIT CIRCLE ILL PLACING POINTS
ON THE UNIT CIRCLE 112 FINDING A MISSING COORDINATE 114 GOING FULL
CIRCLE WITH THE ANGLES 116 STAYING POSITIVE 116 BEING NEGATIVE OR
MULTIPLYING YOUR ANGLES 116 LOCATING AND COMPUTING REFERENCE ANGLES 117
XII TRIGONOMETRY FOR DUMMIES DEFINING TRIG FUNCTIONS FOR ALL ANGLES 121
PUTTING REFERENCE ANGLES TO USE 122 LABELING THE OPTIMISTS AND
PESSIMISTS .122 COMBINING ALL THE RULES 123 USING COORDINATES OF CIRCLES
TO SOLVE FOR TRIG FUNCTIONS 125 CALCULATING WITH COORDINATES ON THE UNIT
CIRCLE 127 CALCULATING WITH COORDINATES ON ANY CIRCLE AT THE ORIGIN 128
DEFINING DOMAINS AND RANGES OF TRIG FUNCTIONS 130 FRIENDLY FUNCTIONS:
SINE AND COSINE 131 CLOSE COUSINS OF THEIR RECIPROCALS: COSECANT AND
SECANT 132 BROTHERS OUT ON THEIR OWN: TANGENT AND COTANGENT 133 CHAPTER
9: APPLYING YOURSELF TO TRIG FUNCTIONS 135 FIRST THINGS FIRST: ELEVATING
AND DEPRESSING 135 ANGLE OF ELEVATION 136 ANGLE OF DEPRESSION 137
MEASURING TALL BUILDINGS WITH A SINGLE BOUND 137 RESCUING A DAMSEL FROM
A TOWER 137 DETERMINING THE HEIGHT OF A TREE 139 MEASURING THE DISTANCE
BETWEEN BUILDINGS 140 MEASURING SLOPE 142 THE SKY'S (NOT) THE LIMIT 143
SPOTTING A BALLOON 144 TRACKING A ROCKET 146 MEASURING THE VIEW OF
SATELLITE CAMERAS 148 CALCULATING ODD SHAPES AND MANEUVERING CORNERS 149
FINDING THE AREA OF A TRIANGULAR PIECE OF LAND 149 MOVING AN OBJECT
AROUND A CORNER 151 PART 111: IDENTITIES \ 155 CHAPTER 10: TRIG'S BASIC
IDENTITIES 157 FLIPPING FUNCTIONS ON THEIR BACKS: RECIPROCAL IDENTITIES
157 FUNCTION TO FUNCTION: RATIO IDENTITIES 159 OPPOSITES ATTRACT:
OPPOSITE-ANGLE IDENTITIES 159 REVISITING THE CLASSIC THEOREM:
PYTHAGOREAN IDENTITIES 162 THE MOTHER OF ALL PYTHAGOREAN IDENTITIES 163
EXTENDING TO TANGENT AND SECANT 164 FINISHING UP WITH COTANGENT AND
COSECANT 165 REARRANGING THE PYTHAGOREAN IDENTITIES .165 COMBINING THE
IDENTITIES 167 THE MANY FACES OF SINE 168 WORKING OUT THE VERSIONS 168
TABLE OF CONTENTS CHAPTER 11: OPERATING ON IDENTITIES 171 SUMMING IT UP
,171 OVERCOMING THE DIFFERENCES 175 DOUBLING YOUR MONEY 179 ONE PLUS ONE
EQUALS TWO SINES 179 THREE'S A CROWD .180 HALVING FUN YET? 182
EXPLAINING THE 183 HALF A TANGENT IS DOUBLE THE FUN 183 USING
HALF-ANGLE IDENTITIES 184 CHAPTER 12: PROVING IDENTITIES 187 LINING UP
THE PLAYERS 187 PICKING SIDES 189 WORKING ON BOTH SIDES 192 GOING BACK
TO SQUARE ONE 194 CHANGING TO SINES AND COSINES 194 FACTORING 197 USING
A LITTLE BIT OF BOTH 198 FRACTURING FRACTIONS 200 BREAKING UP IS HARD TO
DO 200 FINDING A COMMON DENOMINATOR 202 USING TRICKS OF THE TRIG TRADE
203 MULTIPLYING BY A CONJUGATE 204 SQUARING BOTH SIDES 206 IDENTIFYING
WITH THE OPERATIONS 207 ADDING IT UP 207 WHAT DIFFERENCE DOES IT MAKE?
208 MULTIPLYING YOUR FUN 210 HALVING FUN, WISH YOU WERE HERE 211 PART
IV: EQUATIONS AND APPLICATIONS .213 CHAPTER 13: INVESTIGATING INVERSE
TRIG FUNCTIONS 215 WRITING IT RIGHT 215 USING THE NOTATION 216
DISTINGUISHING BETWEEN THE FEW AND MANY 217 DETERMINING DOMAIN AND RANGE
OF INVERSE TRIG FUNCTIONS 219 INVERSE SINE FUNCTION 220 INVERSE COSINE
FUNCTION 220 INVERSE TANGENT FUNCTION 220 INVERSE COTANGENT FUNCTION 220
INVERSE SECANT FUNCTION 221 INVERSE COSECANT FUNCTION 221 SUMMARIZING
DOMAIN AND RANGE 221 TRIGONOMETRY FOR DUMMIES WORKING WITH INVERSES 223
GETTING FRIENDLY WITH YOUR CALCULATOR 224 CHANGING THE MODE
.;.224 INTERPRETING NOTATION ON THE CALCULATOR 225 MULTIPLYING
THE INPUT 227 SOLVING SOME MIXED PROBLEMS 228 CHAPTER 14: SOLVING TRIG
EQUATIONS 231 GENERATING SIMPLE SOLUTIONS 232 FACTORING IN THE SOLUTIONS
233 FINDING A GREATEST COMMON FACTOR 234 FACTORING QUADRATICS. 235
INCREASING THE DEGREES IN FACTORING 237 FACTORING BY GROUPING 239 USING
THE QUADRATIC FORMULA 241 INCORPORATING IDENTITIES 242 FINDING
MULTIPLE-ANGLE SOLUTIONS 245 SQUARING BOTH SIDES 247 MULTIPLYING THROUGH
249 SOLVING WITH A GRAPHING CALCULATOR 249 CHAPTER 15: OBEYING THE LAWS
253 DESCRIBING THE PARTS OF TRIANGLES 253 STANDARDIZING THE PARTS 254
DETERMINING A TRIANGLE 254 FOLLOWING THE LAW OF SINES 256 CONTINUING
WITH THE LAW OF COSINES 260 DEFINING THE LAW OF COSINES 260 LAW OF
COSINES FOR SAS 261 LAW OF COSINES FOR SSS , 263 BEING AMBIGUOUS * 265
INCLUDING THE LAW OF TANGENTS ; 268 FINDING THE AREAS OF TRIANGLES 270
FINDING AREA WITH BASE AND HEIGHT 271 FINDING AREA WITH THREE SIDES 273
FINDING AREA WITH SAS 274 FINDING AREA WITH ASA : 275 PART V: THE GRAPHS
OF TRIG FUNCTIONS. 277 CHAPTER 16: GRAPHING SINE AND COSINE 279 THE ABCS
OF GRAPHING 279 WAVING AT THE SINE 280 DESCRIBING AMPLITUDE AND PERIOD
280 FORMALIZING THE SINE EQUATION 282 TRANSLATING THE SINE 283 TABLE OF
CONTENTS GRAPHING COSINE 285 COMPARING COSINE TO SINE 286 USING
PROPERTIES TO GRAPH COSINE .287 APPLYING THE SINES OF THE TIMES 288
SUNNING YOURSELF 288 AVERAGING TEMPERATURE 290 TAKING YOUR TEMPERATURE
291 MAKING A GOAL 292 THEORIZING WITH BIORHYTHMS 292 CHAPTER 17:
GRAPHING TANGENT AND COTANGENT 295 CHECKING OUT TANGENT 295 DETERMINING
THE PERIOD 296 ASSIGNING THE ASYMPTOTES 296 FIDDLING WITH THE TANGENT V
299 MULTIPLYING THE TANGENT 299 MULTIPLYING THE ANGLE 299 ADDING TO
TANGENT 300 CONFRONTING THE COTANGENT 304 CHAPTER 18: GRAPHING OTHER
TRIG FUNCTIONS 307 SEEING THE COSECANT FOR WHAT IT IS 307 IDENTIFYING
THE ASYMPTOTES 307 USING THE SINE GRAPH 308 VARYING THE COSECANT 310
UNVEILING THE SECANT 312 DETERMINING THE ASYMPTOTES 312 SKETCHING THE
GRAPH OF SECANT 312 FOOLING AROUND WITH SECANT 312 LAYING OUT THE
INVERSE FUNCTIONS 315 GRAPHING INVERSE SINE AND COSINE 316 TAKING ON
INVERSE TANGENT AND COTANGENT 317 CRAFTING INVERSE SECANT AND COSECANT
318 CHAPTER 19: TOPPING OFF TRIG GRAPHS 321 THE BASICS OF TRIG EQUATIONS
321 FLIPPING OVER A HORIZONTAL LINE : 322 INTERPRETING THE EQUATION 323
GRAPHING WITH THE GENERAL FORM 323 ADDING AND SUBTRACTING FUNCTIONS 328
APPLYING YOURSELF TO THE TASK 330 MEASURING THE TIDE 330 TRACKING THE
DEER POPULATION 332 MEASURING THE MOVEMENT OF AN OBJECT ON A SPRING 332
TRIGONOMETRY FOR DUMMIES PART VI: THE PART OF TENS 335 CHAPTER 20: TEN
BASIC IDENTITIES. PLUS ONE 337 RECIPROCAL IDENTITIES 337 RATIO
IDENTITIES 338 PYTHAGOREAN IDENTITIES 338 OPPOSITE-ANGLE IDENTITIES 338
CHAPTER 21: TEN NOT-SO-BASIC IDENTITIES 341 PRODUCT-TO-SUM IDENTITIES
341 SUM-TO-PRODUCT IDENTITIES 342 REDUCTION FORMULA 343 MOLLWEIDE'S
EQUATIONS 343 CHAPTER 22: TEN WAYS TO FIND THE AREA OF A TRIANGLE 345
USING THE BASE AND HEIGHT 346 ACQUAINTING YOURSELF WITH HERON 346
APPLYING TRIG (THE WHOLE POINT OF THIS BOOK) 346 ) SIDE-ANGLE-SIDE
FORMULAS. 347 ANGLE-SIDE-ANGLE FORMULAS 347 GOING BACK TO ALGEBRA: USING
DETERMINANTS 347 CHAPTER 23: TEN SINE CURVES REPRESENTING MONTHLY
TEMPERATURES 349 BOSTON, MASSACHUSETTS 349 CHICAGO, ILLINOIS 350 DENVER,
COLORADO 350 FAIRBANKS, ALASKA 350 GALVESTON, TEXAS 350 HONOLULU, HAWAII
':. 350 MIAMI, FLORIDA 351 SAN DIEGO, CALIFORNIA. 351 SAN JUAN,
PUERTO RICO 351 SAULT STE. MARIE, MICHIGAN 351 APPENDIX: TRIG FUNCTIONS
TABLE 353 INDEX 357 |
| any_adam_object | 1 |
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| callnumber-first | Q - Science |
| callnumber-label | QA531 |
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| dewey-full | 516.24 |
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| dewey-ones | 516 - Geometry |
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| dewey-search | 516.24 |
| dewey-sort | 3516.24 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Book |
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| index_date | 2024-07-02T16:53:40Z |
| indexdate | 2024-07-09T20:54:24Z |
| institution | BVB |
| isbn | 0764569031 |
| language | English |
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| spelling | Sterling, Mary Jane 1944- Verfasser (DE-588)131547666 aut Trigonometry for dummies by Mary Jane Sterling Indianapolis, Ind. Wiley c2005 XVI, 368 S. Ill., graph. Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier --For dummies Includes index Trigonometry Trigonometrie (DE-588)4060888-8 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content Trigonometrie (DE-588)4060888-8 s DE-604 http://www.loc.gov/catdir/enhancements/fy0620/2004116322-b.html Contributor biographical information http://www.loc.gov/catdir/enhancements/fy0620/2004116322-d.html Publisher description http://www.loc.gov/catdir/enhancements/fy0620/2004116322-t.html Table of contents only GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015506840&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Sterling, Mary Jane 1944- Trigonometry for dummies Trigonometry Trigonometrie (DE-588)4060888-8 gnd |
| subject_GND | (DE-588)4060888-8 (DE-588)4151278-9 |
| title | Trigonometry for dummies |
| title_auth | Trigonometry for dummies |
| title_exact_search | Trigonometry for dummies |
| title_exact_search_txtP | Trigonometry for dummies |
| title_full | Trigonometry for dummies by Mary Jane Sterling |
| title_fullStr | Trigonometry for dummies by Mary Jane Sterling |
| title_full_unstemmed | Trigonometry for dummies by Mary Jane Sterling |
| title_short | Trigonometry for dummies |
| title_sort | trigonometry for dummies |
| topic | Trigonometry Trigonometrie (DE-588)4060888-8 gnd |
| topic_facet | Trigonometry Trigonometrie Einführung |
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