Index
A211
A
Absolute value
of a complex number, 468
inequality, A67
solution of, A67
properties of, A6
of a real number, A5
Acute angle, 281
Addition
of complex numbers, 160
of fractions
with like denominators, A10
with unlike denominators, A10
of matrices, 585
properties of, 587
vector, 447, 817
parallelogram law for, 447
properties of, 449
resultant of, 447
Additive identity
for a complex number, 160
for a matrix, 588
for a real number, A8
Additive inverse, A8
for a complex number, 160
for a real number, A8
Adjacent side of a right triangle, 299
Adjoining matrices, 601
Algebraic expression, A7
domain of, A39
equivalent, A39
evaluate, A7
term of, A7
Algebraic function, 216
Algebraic properties of the cross
product, 825, 845
Algebraic tests for symmetry, 17
Alternative definition of conic, 791
Alternative form of Law of Cosines,
437, 488
Ambiguous case (SSA), 430
Amplitude of sine and cosine curves, 321
Analytic geometry, solid, 810
Angle(s), 280
acute, 281
between two lines, 727, 728
between two planes, 834
between two vectors, 459, 490
in space, 818
central, 281
complementary, 283
conversions between degrees and
radians, 284
coterminal, 280
degree measure of, 283
of depression, 304
direction, of a vector, 451
of elevation, 304
initial side of, 280
measure of, 281
negative, 280
obtuse, 281
positive, 280
radian measure of, 281
reference, 312
of repose, 349
standard position, 280
supplementary, 283
terminal side of, 280
vertex of, 280
Angular speed, 285
Annuity, increasing, 666
Aphelion distance, 749, 796
Apogee, 746
“Approximately equal to” symbol, A1
Arc length, 285
Arccosine function, 343
Arcsine function, 341, 343
Arctangent function, 343
Area
common formulas for, A59
of an oblique triangle, 432
of a plane region, 894
problem, 893
of a sector of a circle, 287
of a triangle
using a determinant, 619
Heron’s Area Formula, 440, 489
Argument of a complex number, 469
Arithmetic combination of functions, 83
Arithmetic mean, 650
Arithmetic sequence, 651
common difference of, 651
th partial sum of, 655
th term of, 652
recursion formula, 653
sum of a finite, 654, 721
Associative Property of Addition
for complex numbers, 161
for matrices, 587
for real numbers, A8
Associative Property of Multiplication
for complex numbers, 161
for matrices, 591
for real numbers, A8
Associative Property of Scalar
Multiplication for matrices,
587, 591
Astronomical unit, 794
Asymptote(s)
horizontal, 182
of a hyperbola, 753
oblique, 187
of a rational function, 183
slant, 187
vertical, 182
Augmented matrix, 571
Average rate of change, 59, 876
Average value of a population, 259
Axis (axes),
conjugate, of a hyperbola, 753
imaginary, 468
major, of an ellipse, 742
minor, of an ellipse, 742
of a parabola, 127, 734
polar, 777
real, 468
rotation of, 761
of symmetry, 127
transverse, of a hyperbola, 751
B
Back-substitution, 495
Base, A14
natural, 220
Basic conics, 733
circle, 733
ellipse, 733
hyperbola, 733
parabola, 733
Basic equation of a partial fraction
decomposition, 531
guidelines for solving, 535