Index Index
\(\bar{z}\). See complex conjugate
\(\pi\), Paragraph
\(\theta\), Assemblage. See also Greek alphabet; polar coordinates
\(\|{\bf{v}}\|\). See magnitude of a vector
acos, Paragraph. See also inverse cosine
addition formula, Assemblage Paragraph Exercises. See also sum of angles
algebraic expression, Item. See also expression
alternate interior angles, Subsection
altitude
of a triangle, Paragraph
ambiguous case, Note Exercises Subsection Assemblage Assemblage
amplitude, Item Assemblage Assemblage
angle, Section Paragraph Subsection
acute, Item (see also acute angle)
alternate interior, Subsection (see also alternate interior angles)
as rotation, Section
between vectors, Assemblage
central, Item
complementary, Item (see also complementary angles)
converting measurement units, Assemblage
corresponding, Paragraph (see also corresponding angles)
coterminal, Subsection
exterior, Exercises
find, Subsection Subsection Subsection
in radians, Subsection (see also radian)
inscribed, Item
of incidence, Paragraph
of inclination, Assemblage (see also angle of inclination)
of refraction, Paragraph
reference, Subsection Paragraph (see also reference angle)
right, Paragraph
special, Subsection Paragraph Paragraph Subsection
standard position, Subsection Paragraph Subsection
straight, Paragraph
sum in a triangle, Assemblage
supplementary, Item Subsection (see also supplementary angles)
vertical, Paragraph (see also vertical angles)
angle of inclination, Subsection Assemblage
arccos, Paragraph. See also inverse cosine
arclength, Paragraph Section Subsection Assemblage
formula, Subsection Assemblage
arcsin, Subsection. See also inverse sine
arctan, Paragraph. See also inverse tangent
area
of circle, Assemblage
of triangle, Subsection Assemblage
argument, Assemblage
asin, Paragraph. See also inverse sine
astronomical unit (AU), Paragraph
atan, Paragraph. See also inverse tangent
bearing, Subsection Subsection
center, Paragraph
circle, Paragraph
area, Assemblage
circumscribing, Item
equation, Subsection Assemblage
circular function, Assemblage
circumference, Subsection Assemblage
complex conjugate, Paragraph Definition
complex number, Section Subsection Assemblage
difference of, Assemblage
graphing, Subsection
length, Paragraph (see also modulus)
polar form, Assemblage
product of, Assemblage
quotient of, Subsection Assemblage
sum of, Assemblage
complex plane, Subsection
component, Subsection Subsection Paragraph Paragraph Subsection Assemblage Assemblage. See also vector
coordinate form, Subsection Assemblage
vector component, Caution
conclusion, Item
congruent triangles, Subsection Paragraph
conjugate. See complex conjugate
converse, Item
conversions equations, Assemblage Subsection
coordinates of point, Assemblage. See also polar coordinates
corresponding angles, Paragraph
cos \(\theta\), Definition. See also cosine
cos \(\vphantom{t}^{-1}\), Paragraph Definition. See also inverse trigonometric function
cosecant, Definition
cosine, Subsection Definition
of a real number, Subsection Assemblage Assemblage
cosine function, Subsection. See also cosine
cosine ratio, Subsection. See also trigonometric ratios
cotangent, Definition
cotangent identity, Assemblage
coterminal angles, Subsection
DeMoivre’s Theorem, Assemblage
difference of angles, Assemblage Assemblage Exercises Exercise. See also trigonometric identity
discriminant, Paragraph
distance formula, Subsection Assemblage
domain, Paragraph Assemblage
of inverse function, Assemblage
restrict, Subsection Paragraph
dot product, Subsection Assemblage Paragraph
geometric form, Subsection Assemblage
double angle formulas, Paragraph. See also double angle identity
double angle identity, Subsection Assemblage
for cosine, Assemblage
equation, Assemblage
conditional, Paragraph
trigonometric, Subsection (see also trigonometric equation)
equilateral triangle, Paragraph
angles of, Assemblage
equilibrium, Paragraph
equivalent, Assemblage
evaluate, Item
expression, Item
trigonometric, Subsection (see also trigonometric expression)
facts from geometry, Assemblage
FOIL (acronym: First, Outside, Inside, Last), Paragraph
force, Paragraph
function
notation, Subsection Paragraph
sinusoidal, Subsection
fundamental theorem of algebra, Assemblage
Greek alphabet, Table
horizontal line test, Assemblage
horizontal shift, Assemblage
hypotenuse, Paragraph Subsection
hypothesis, Item
identity, Subsection Paragraph Assemblage
check graphically, Subsection
proving, Subsection
Pythagorean, Subsection (see also Pythagorean identity)
with trigonometric ratios, Subsection (see also trigonometric identity)
imaginary
axis, Subsection
number, Subsection Assemblage
part, Paragraph
unit, Assemblage
initial side of an angle in standard position, Item
input variable, Subsection Paragraph
inverse
function, Section Subsection Paragraph Caution (see also inverse trigonometric function)
graph of, Subsection
operation, Paragraph (see also inverse)
inverse cosine, Definition
inverse sine, Definition
inverse tangent, Definition
inverse trigonometric function, Paragraph Section Assemblage. See also inverse cosine; inverse sine; inverse tangent
irrational number, Subsection Definition
isosceles triangle, Paragraph
base angles, Assemblage
law of cosines, Section Assemblage Exercise Exercise
law of sines, Section Assemblage Activity
leg, Paragraph Subsection
Lissajous figure, Paragraph
loudness, Item
magnitude of a vector, Paragraph
mathematical model, Paragraph
Mercator map, Chapter
and secant function, Paragraph
midline, Item Assemblage Assemblage
minute (as a measure of angle), Assemblage
modulus, Paragraph Assemblage Assemblage
normal line, Paragraph
oblique triangle, Paragraph Item Subsection Assemblage
one-to-one, Paragraph
opposite vector, Paragraph
orthogonal, Item
parallax, Subsection Paragraph
parallelogram rule, Paragraph
parameter, Paragraph
parsec, Checkpoint
period, Paragraph Assemblage Assemblage Assemblage
periodic function, Subsection Paragraph Paragraph Assemblage Section Subsection Assemblage
pitch of musical note, Item
polar axis, Paragraph
polar coordinates, Paragraph Assemblage
\(\theta\), Assemblage
\(r\), Assemblage
angle, Assemblage
converting Cartesian, Subsection
distance, Assemblage
equations, Subsection
graphing, Section
non-uniqueness, Assemblage
polar form, Section Subsection Assemblage
product, Assemblage
quotient, Assemblage
polar graphs, Section
catalog of curves, Subsection
pole, Paragraph
polygon
regular, Exercises
pure imaginary number. See imaginarynumber
Pythagorean identity, Subsection Assemblage Exercise Assemblage Assemblage Exercise Exercise
alternate forms, Assemblage
Pythagorean theorem, Subsection Exercise Paragraph
converse, Note
quadrantal angles, Paragraph
quadratic formula, Assemblage
radius, Paragraph
range, Paragraph Assemblage
of inverse function, Assemblage
rational number, Subsection Definition
real axis, Subsection
real part, Paragraph
reciprocal function, Subsection Assemblage Assemblage Activity. See also cosecant; cotangent; secant
graph, Subsection
reciprocal ratio, Activity. See also reciprocal function
reciprocal trigonometric function, Assemblage. See also reciprocal function
reciprocal trigonometric ratios, Assemblage. See also reciprocal function
rectangular coordinate system, Paragraph
reference angle, Subsection Paragraph Note Activity Subsection Assemblage Assemblage
reference triangle, Paragraph
repeating decimal, Paragraph. See also rational number
resultant force, Paragraph
right angle, Paragraph
right triangle, Assemblage. See also triangle
Pythagorean theorem, Subsection
similar, Subsection
solving, Section Subsection
trigonometry, Section
rotation, Section Subsection
SAA (one side and two angles), Assemblage
SAS (two sides and included angle), Assemblage
scalar, Paragraph
multiplication, Subsection Paragraph Assemblage (see also vector)
scalar product, Paragraph. See also dot product
scale a vector, Assemblage. See also vector
scalene triangle, Exercise
secant, Definition
Mercator map, Paragraph
second (as a measure of angle), Assemblage
sector, Paragraph
self-similarity, Paragraph
similar triangles, Section Paragraph Assemblage
proportions, Subsection
right triangles, Subsection
simplify, Assemblage
sin \(\theta\), Subsection. See also sine
sin \(\vphantom{t}^{-1}\), Paragraph Definition. See also inverse trigonometric function
sine, Subsection Definition
of a real number, Subsection Assemblage Assemblage
of an acute angle, Definition
using to find an unknown side, Subsection
sine function, Subsection. See also sine
sine ratio, Note Subsection. See also sine; trigonometric ratios
sinusoidal function, Subsection
graph, Subsection
standard form, Assemblage
slope, Subsection
Snell’s Law, Subsection Subsection
solve
a triangle, Paragraph Assemblage
an equation, Assemblage
an equation using a graph, Paragraph
inequality, Example
right triangle, Section
trigonometric equations, Subsection (see also trigonometric equation)
special angles, Subsection
radians, Subsection
supplements of, Subsection
SSA (two sides and non-included angle), Assemblage
SSS (three sides), Assemblage
straight angle, Paragraph
substitution
to solve trigonometric equations, Subsection Assemblage
subtend, Item
subtraction formula, Assemblage. See also difference of angles
sum of angles, Assemblage Assemblage Exercises. See also trigonometric identity
trigonometric ratios of, Subsection Assemblage
tan \((\theta)\), Definition. See also tangent
tan \(\theta\), Paragraph
tan \(\vphantom{t}^{-1}\), Paragraph Definition. See also inverse trigonometric function
tangent, Subsection Paragraph Definition
of a real number, Assemblage
tangent function, Subsection Subsection Subsection. See also tangent
tangent identity, Subsection Assemblage Exercise Assemblage
tangent ratio, Subsection. See also trigonometric ratios
terminal side of an angle in standard position, Item
terminating decimal, Paragraph. See also rational number
timbre, Item
transformation, Paragraph
combining, Subsection
horizontal shift, Assemblage
triangle, Section Subsection
altitude, Paragraph
angle sum, Assemblage
area of, Subsection Assemblage
equilateral, Paragraph (see also equilateral triangle)
exterior angle, Exercises
inequality, Assemblage
isosceles, Paragraph (see also isosceles triangle)
oblique, Paragraph (see also oblique triangle)
overlapping, Subsection
reference, Paragraph
right, Assemblage
scalene, Exercise
similar, Paragraph Assemblage (see also similar triangles)
solving, Subsection Assemblage
triangle inequality, Subsection Assemblage
triangulation, Paragraph
trigonometric equation, Note Subsection Subsection
graphical solutions, Subsection
with squares of trig ratios, Subsection
trigonometric expression, Subsection
factoring, Subsection
simplifying, Subsection
trigonometric function, Chapter. See also trigonometric ratios
graph, Section
product of, Subsection
raising to power, Subsection Assemblage Paragraph
trigonometric identity, Subsection Assemblage Subsection
difference of angles, Assemblage
double angle, Assemblage Assemblage
sum and difference for tangent, Assemblage
sum of angles, Subsection Assemblage
trigonometric ratios, Assemblage Assemblage
coordinate definition, Assemblage
for all angles, Subsection Assemblage
obtuse angle, Activity Subsection
supplementary angles, Subsection Assemblage
trigonometry
right triangle, Section
unit circle, Definition Subsection Paragraph Activity
angles in, Assemblage Assemblage
arclength and radians, Subsection
coordinates of point, Assemblage Assemblage
adding, Assemblage Subsection Assemblage
angle between, Assemblage
component, Assemblage Caution (see also component)
coordinate form, Section Assemblage
displacement, Paragraph
geometric vs coordinate form, Subsection Assemblage
notation, Subsection
operations on, Assemblage (see also scale; vector; adding)
opposite, Paragraph
position, Paragraph
resultant, Paragraph
scaling, Assemblage Assemblage
unit, Subsection Assemblage
zero, Paragraph
velocity, Subsection
vertex angle
of an isosceles triangle, Paragraph
vertical angles, Paragraph Assemblage
zero of a polynomial, Subsection Assemblage
zero vector, Paragraph
