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| McKeague C. P. — Trigonometry |
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| Предметный указатель |
15°-75°-90° triangles 108
30°-60°-90° triangles 7
45°-45°-90° triangles 9
Absolute value 399 438
Accuracy of angles 71 105
Accuracy of sides 71 105
Acute angles 3
Acute angles, trigonometric functions 63—64
Acute triangles 4
Addition and subtraction, algebraic vectors 370—371 384
Addition and subtraction, complex numbers 392 437
Addition and subtraction, vectors 94 106
Addition property of equality 300
Agnesi, Maria Gaetana 336
Ailles rectangle 108
Airspeed 353
Algebra-geometry association 14
Algebraic approach to vectors 369—375
Algebraic signs of trigonometric functions 29 48
Algebraic vectors 370—371 373 384
Ambiguous case 348—349 383
Amplitude 172 185—186 249
Amplitude, amplitude and period for sine and cosine 190
Analytic geometry 15
Angle of depression 81 105
Angle of elevation 81 105
angles 45
Angles between vectors 378—379
Angles, accuracy 71 105
Angles, Acute 3
Angles, acute, trigonometric functions 63—64
Angles, Complementary 3
Angles, Coterminal 21 47
Angles, degree measure of angles 3—4 46
Angles, double-angle formulas 275 276 278 295
Angles, half-angle formulas 282 284 295
Angles, initial side 3
Angles, multiple angles and equations 313—318 333
Angles, Negative 3
Angles, Obtuse 3
Angles, Positive 3
Angles, Quadrantal 21
Angles, Reference 110 162
Angles, related 110
Angles, right 1 3
Angles, special 57 104
Angles, standard position 20—21 47
Angles, straight 3
Angles, supplementary 3—4
Angles, terminal side 3
Angles, triangles see "Triangles"
Angular frequency 195
Angular velocity 151 164
Antilogarithm 470
Apparent diameter 149—150
Approximations of functions 113—114
Arc length 140 163
Arccosine 242
Archimedes 427
Arcsine 242
Arctangent 242
Area of sectors 143—144 164
Area of triangles 383—384
Area of triangles, three sides 366
Area of triangles, two angles and one side 365
Area of triangles, two sides and included angle 364
Arendt, Hannah 337
Argand, Jean Robert 442
Argument of complex numbers 399 438
Aristotle 52
Aryabhata 129
Asymptotes 175 177—178
Basic identities 294
Bearing of a line 84 105
Bloom, Allan 14
Bombelli, Rafael 442
Cable care 109
Calculators and degree mode 63—64
Cardan, Jerome 389 398 442
Cardan, Jerome, Cardan's formula 398
Cardano, Girolamo see "Cardan Jerome"
Cartesian coordinate system 14
Change of base 494—495
Characteristic 488
circles 18—20 47
Circles, equation 19
Circular functions 129—140 163
Circular functions, definition 131
Circular functions, domains 135 163
Circular functions, geometric representations 136
Circular functions, ranges 135 163
Cofunction theorem 56 104
Cofunctions 55 56
Combinations of functions, graphing 231—237
Common logarithms 487—490
Complement 3
Complementary angles 3
Complex conjugates 394 437
Complex numbers, absolute value 399 438
Complex numbers, addition and subtraction 392 437
Complex numbers, argument 399 438
Complex numbers, complex conjugates 394 437
Complex numbers, definition 390 391 437
Complex numbers, equality 392 437
Complex numbers, graphing 398 438
Complex numbers, imaginary part 391 437
Complex numbers, imaginary unit 390
Complex numbers, modulus 399
Complex numbers, multiplication and division 393 404—408 437
Complex numbers, powers of i 393 438
Complex numbers, roots 410—412 439
Complex numbers, trigonometric form 398—401 438
Component form of vectors 369 372
Compound interest 468 471 499
Conditional equations 300
Continuously compounded interest 469
Contour lines 52
Conversion factors 154
Cosecant 212—215
Cosecant graphs 177—178
Cosine 55
Cosine and sine functions, graphing 204
Cosine graphs 173—175
Cosines, Law of 356 383
Cosines, law of derivation 357
Cosines, law of three sides 358—359
Cosines, law of two sides and included angle 357—358
Cotangent and tangent 208—212
Cotangent and tangent functions, graphing 212
Cotangent graphs 178—179
Coterminal angles 21 47
Cotes, Roger 118
Cycloid 334—335
De Moivre, Abraham 405 442
de Moivre, Abraham, de Moivre's theorem 405 439
Decibel 482
Decimal degrees 62 105
Degree measure of angles 3—4 46
Degree mode and calculators 63—64
DEGREES 3 61—62 104
Degrees, converting from radians 121 123
Degrees, converting to radians 120 123
Degrees, radians and degrees 117—129 163
Dependent variable 448
Descartes, Rene 14
Descartes, Rene, Cartesian coordinate system 14
Devlin, Keith 169
Difference and sum formulas 267—269 271 294
Direction 84 105
Distance formula 17—18 46
| Domain 135 445 446 447
Domains of circular functions 135 163
Dot product 378—381 385
Double-angle formulas 275 276 278 295
Doubling time 494
Einstein, Albert 369
Einstein, Albert, theory of relativity 62 369
Eliminating the parameter 324
Equality for complex numbers 392 437
Equality for vectors 94
Equations, circles 19
Equations, conditional 300
Equations, from graphs 218—221
Equations, multiple angles 313—318 333
Equations, parametric 322 333
Equations, polar coordinates 424—425 440
Equations, trigonometric 300—305 308—311 332—333
Equilateral triangles 4
Equivalent forms, Pythagorean identities 36
Equivalent forms, reciprocal identities 34
Euler, Leonhard 442
Even functions 180—182 250
Exponential equations 495 498
Exponential form 475
Ferris wheel 70—71
Ferris, George W.G. 70
Foot-pound 100
force 98
Fourier series 234
frequency 196
Function(s) 237
Function(s), even and odd 180—182
Function(s), exponential 464—465
Function(s), inverse 237 238 288 459 463
Function(s), inverse trigonometric 237—242
Function(s), logarithmic 474 476—477
Function(s), notation 448—449
Function(s), one-to-one 238 458
Function(s), trigonometric 26—27 29 54 56 63—64 131 208—209
Galileo 109
Geometric representations of circular functions 136
Geometry-algebra association 14
Golden ratio 14
Graphing, combinations of functions 231—237
Graphing, complex numbers 398 438
Graphing, inverse 457—458
Graphing, lines 15—16
Graphing, parabolas 16—17
Graphing, sine and cosine functions 204
Graphing, tangent and cotangent functions 212
Graphs, cosecant 177—178
Graphs, cosine 173—175
Graphs, cotangent 178—179
Graphs, equations from graphs 218—221
Graphs, equations in polar coordinates 427—435
Graphs, secant 178—179
Graphs, sine 170—173
Graphs, tangent 175—176
Graphs, trigonometric functions 179
Grassmann, Hermann 369
Gravity Probe B 62
Great circle 124
Ground speed 353
Half-angle formulas 282 284 295
Hallidie, Andrew Smith 109
Hamilton, Sir William Rowan 93 369 388
Heading 352 383
Heron of Alexandria 366
Heron's formula 366
Hertz 196
Hipparchus 108 129
Horizontal vector components 96 106 369 372—373
Hypotenuse 5
Identities, basic 294
Identities, involving inverse functions 288—289
Identities, proving 256—258 294
Identities, Pythagorean 35—36 48 257 294
Identities, ratio 34—35 48 257 294
Identities, reciprocal 33—34 48 257 294
Identities, trigonometric equations 333
Imaginary axis 399
Imaginary number 391
Imaginary part of complex numbers 391 437
Imaginary unit 390
Independent variable 448
Initial side of angles 3
Inverse function notation 238 459
Inverse of a relation 455
Inverse trigonometric functions 242 251
Inverse trigonometric functions, cosine 240—241
Inverse trigonometric functions, definitions 237
Inverse trigonometric functions, identities and formulas 288—289
Inverse trigonometric functions, Notation 238
Inverse trigonometric functions, sine 239—240
Inverse trigonometric functions, tangent function 241
Isosceles triangles 4
Law of Cosines 356 383
Law of cosines, derivation 357
Law of cosines, three sides 358—359
Law of cosines, two sides and included angle 357—358
Law of Sines 338—339 383
Law of sines, ambiguous case 348—349 383
Law of sines, two angles and one side 340
Legs of right triangle 5
Lichtenberg, Georg C. 299
Linear velocity 150 164
Lines of sight 82
Lines, graphing 15—16
Logarithmic form 475
Logarithms 474—475
Logarithms, change of base 494—495
Logarithms, common 487—488
Logarithms, identities 477
Logarithms, natural 487—488
Logarithms, properties of 482—483
Magnitude of vectors 370 384
Mantissa 488
McClure, William 153
Melville, Herman 335
Minutes 61—62 104
Modulus 399
Multiple angles and equations 313—318 333
Multiplication and division with complex numbers 393 437
Multiplication property of equality 300
Natural logarithm 490—491
Navigation 124 352—353 383
Negative angles 3
Oblique triangles 338
Obtuse angles 3
Obtuse triangles 4
Odd functions 180—182 250
One-to-one function 238 458
Parabolas, graphing 16—17
Parameters 322
Parameters, eliminating 324
Parametric equations 322 329 333
Pascal, Blaise 14
Period 172 187—188
Period, amplitude and period for sine and cosine 190
Period, period and phase shift for sine and cosine 203
Period, period and phase shift for tangent and cotangent 212
Periodic functions 249
Perpendicular vectors 380 385
pH formula 486
Phase shift 200—202 250
Phase shift, period and phase shift for sine and cosine 203
Phase shift, period and phase shift for tangent and cotangent 212
Plane curves 322
Poincare, Henri 389
Polar axis 418
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