## Index Index

\(\bar{z}\).

*See*complex conjugate
\(\pi\), Paragraph

\(\theta\), Assemblage.

*See also*Greek alphabet; polar coordinates
\(\|{\bf{v}}\|\).

*See*magnitude of a vectoracos, Paragraph.

*See also*inverse cosineaddition formula, Assemblage Paragraph Exercises.

*See also*sum of anglesalgebraic expression, Item.

*See also*expressionalternate 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 cosinearclength, Paragraph Section Subsection Assemblage

formula, Subsection Assemblage

arcsin, Subsection.

*See also*inverse sinearctan, Paragraph.

*See also*inverse tangentarea

of circle, Assemblage

of triangle, Subsection Assemblage

argument, Assemblage

asin, Paragraph.

*See also*inverse sineastronomical unit (AU), Paragraph

atan, Paragraph.

*See also*inverse tangentbearing, 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*vectorcoordinate form, Subsection Assemblage

vector component, Caution

conclusion, Item

congruent triangles, Subsection Paragraph

conjugate.

*See*complex conjugateconverse, Item

conversions equations, Assemblage Subsection

coordinates of point, Assemblage.

*See also*polar coordinatescorresponding angles, Paragraph

cos \(\theta\), Definition.

*See also*cosinecos \(\vphantom{t}^{-1}\), Paragraph Definition.

*See also*inverse trigonometric functioncosecant, Definition

cosine, Subsection Definition

of a real number, Subsection Assemblage Assemblage

cosine function, Subsection.

*See also*cosinecosine ratio, Subsection.

*See also*trigonometric ratioscotangent, Definition

cotangent identity, Assemblage

coterminal angles, Subsection

DeMoivre’s Theorem, Assemblage

difference of angles, Assemblage Assemblage Exercises Exercise.

*See also*trigonometric identitydiscriminant, 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 identitydouble 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 tangentirrational 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*imaginarynumberPythagorean 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; secantgraph, Subsection

reciprocal ratio, Activity.

*See also*reciprocal functionreciprocal trigonometric function, Assemblage.

*See also*reciprocal functionreciprocal trigonometric ratios, Assemblage.

*See also*reciprocal functionrectangular coordinate system, Paragraph

reference angle, Subsection Paragraph Note Activity Subsection Assemblage Assemblage

reference triangle, Paragraph

repeating decimal, Paragraph.

*See also*rational numberresultant force, Paragraph

right angle, Paragraph

right triangle, Assemblage.

*See also*trianglePythagorean 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 productscale a vector, Assemblage.

*See also*vectorscalene 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*sinesin \(\vphantom{t}^{-1}\), Paragraph Definition.

*See also*inverse trigonometric functionsine, 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*sinesine ratio, Note Subsection.

*See also*sine; trigonometric ratiossinusoidal 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 anglessum of angles, Assemblage Assemblage Exercises.

*See also*trigonometric identitytrigonometric ratios of, Subsection Assemblage

tan \((\theta)\), Definition.

*See also*tangenttan \(\theta\), Paragraph

tan \(\vphantom{t}^{-1}\), Paragraph Definition.

*See also*inverse trigonometric functiontangent, Subsection Paragraph Definition

of a real number, Assemblage

tangent function, Subsection Subsection Subsection.

*See also*tangenttangent identity, Subsection Assemblage Exercise Assemblage

tangent ratio, Subsection.

*See also*trigonometric ratiosterminal side of an angle in standard position, Item

terminating decimal, Paragraph.

*See also*rational numbertimbre, 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 ratiosgraph, 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