Index
ALPHABETICAL LIST OF CONCEPTS WITH PROBLEM NUMBERS
This comprehensive index organizes the concepts and skills discussed within the book alphabetically. Each entry is accompanied by one or more problem numbers, in which the topics are most prominently featured.
All of these numbers refer to problems, not pages, in the book. For example, 4.9 is the ninth problem in Chapter 4.
Numbers & Symbols
30°–60°–90° triangle: 1.34, 3.10–3.21, 12.6, 12.8–12.10, 12.21
45°–45°–90° triangle: 2.7, 3.1–3.9, 12.7, 12.15–12.16, 15.40
π/4–π/4–π/2 triangle: see 45°–45°–90° triangle
π/6–π/3–π/2 triangle: see 30°–60°–90° triangle
A
absolute value
(of a) complex number: 18.13
(of a) real number: 8.26–8.27
adding
complex numbers: 18.6
vectors (algebraically): 15.12, 15.15, 15.17, 15.20, 15.29, 16.48
vectors (graphically): 15.1–15.11, 15.14, 15.27, 16.41, 16.44
adjacent leg: 2.15–2.16, 2.18–2.23, 2.43–2.44, 3.14
ambiguous case: 13.9–13.12
amplitude: 5.4, 5.8, 5.11, 5.31
angle
between vectors: 16.19–16.27, 16.29, 16.36
complementary: 1.31–1.34
converting units of measure: 1.20–1.30
coterminal: 4.16–4.29
degrees: 1.10, 1.14, 1.16
initial side: 1.6–1.8
minutes/seconds: 1.18–1.19
naming: 1.2
negative: 1.17, 1.26, 1.28
radians: 1.11–1.14, 1.17
reference: 4.1–4.5, 4.30, 4.33, 4.37, 4.44, 7.45
revolutions: 1.9, 1.14–1.15
right: 1.14
standard position: 1.3–1.8, 1.14
straight: 1.35–1.37
supplementary: 1.35–1.39
terminal side: 1.6–1.8, 1.15–1.17, 3.34, 3.36, 4.36, 4.40, 4.44
angular coordinate: 17.16, 17.45
arc
central angle: 1.40–1.45
length: 1.41–1.45, 12.37, 12.42
major: 1.45
measure: 1.40
minor: 1.45
radius: 1.41–1.45
arccosine: 9.5–9.8, 9.21, 9.23, 9.25, 11.25–11.26, 13.16, 13.21
arcsecant: 9.25
arcsine: 9.9–9.11, 9.17, 9.20, 9.22, 9.24, 12.43, 13.11, 13.17, 13.19
arctangent: 9.12–9.14, 9.19, 9.26, 11.12, 11.21, 11.35
area of a triangle
AAS: 12.19–12.20
ASA: 12.19, 12.22–12.24
base and height: 12.1–12.12, 12.15, 12.21, 12.28
Heron’s formula: 12.25–12.27, 12.29–12.34, 12.44, 13.24
SAS: 12.14, 12.16–12.18, 12.24, 13.22
SSS: 12.25–12.27, 12.29–12.34, 12.44, 13.24
argument: 18.15, 18.19
asymptote: 5.10, 6.2, 6.7, 6.12, 6.17, 9.14
B–C
base: 12.1–12.12, 12.15, 12.21, 12.28
calculator-based values: 2.37–2.45
central angle: 1.40–1.45, 12.35, 12.37–12.39, 12.41, 12.43
circle: 12.35–12.45, 17.12, 17.43–17.44
circumference: 1.13, 1.42, 12.40
cofunction identity: 7.1–7.4, 7.6, 7.11–7.12, 7.17–7.18, 7.40–7.41, 8.16
commutative: 15.5, 16.5–16.6
complementary angles: 1.31–1.34
complex fraction: 2.28
complex number
absolute value: 18.13
adding: 18.6
argument: 18.15, 18.19
conjugate: 18.2, 18.4, 18.9, 18.12, 18.30
De Moivre’s theorem: 18.33, 18.35–18.39
dividing: 18.9, 18.12, 18.28, 18.30–18.32, 18.39
imaginary part: 18.1
modulus: 18.13–18.14, 18.18
multiplying: 18.8, 18.11, 18.23, 18.25–18.27, 18.38
plot: 18.3–18.4
real part: 18.1
rectangular form: 18.1–18.17, 18.21–18.22, 18.24–18.25, 18.29–18.30, 18.34
roots: 18.40–18.45
trigonometric form: 18.16, 18.18–18.23, 18.26–18.28, 18.31–18.33, 18.35–18.45
component form: 14.12–14.24, 14.31–14.32, 15.19–15.20, 15.38–15.44
compression: see graphing transformations
conjugate: 18.2, 18.4, 18.9, 18.12, 18.30
conversion fraction: 1.20–1.30
converting
between degrees and radians: 1.24–1.30
between degrees and revolutions: 1.20–1.21
between minutes/seconds to decimal form: 1.18–1.19
between parametric and rectangular form: 17.4, 17.7, 17.10, 17.12, 17.14
between polar and rectangular form: 17.30–17.42, 17.46–17.47
between radians and revolutions: 1.22–1.23
coordinate plane: 2.8, 3.5–3.8, 3.17–3.22
cosecant: 2.22, 2.24, 3.43, 4.39, 4.44, 6.16–6.20
cosine: 2.18, 2.20, 2.26, 2.27–2.28, 2.43, 3.14, 3.22, 3.24, 3.26, 3.28, 3.30, 3.32, 3.35, 3.39–3.40, 4.4, 4.28, 4.32, 4.37, 4.43, 5.35–5.41, 6.11, 12.12, 15.37–15.44
cotangent: 2.21, 2.25, 3.42, 4.29, 4.38, 4.42, 4.45, 6.6–6.10
coterminal angles: 4.16–4.29
cube root: 18.43–18.44
D–E–F
De Moivre’s theorem: 18.33, 18.35–18.39
degrees: 1.10, 1.14, 1.16
diameter: 1.13, 1.42, 1.44
difference of perfect squares: 8.13, 8.41, 10.17, 10.21
direction angle (of a vector): 14.44–14.48, 14.50–14.51, 15.37–15.44
displacement: 16.49–16.52
distributive: 16.9–16.16
dividing complex numbers: 18.9, 18.12, 18.28, 18.30–18.32, 18.39
domain: 5.1, 5.6, 5.10, 6.2, 6.4, 6.7, 6.11, 6.16, 9.7, 9.11, 9.14
dot product
alternate version: 16.17, 16.21–16.27, 16.29–16.30
modified version: 16.35–16.36
standard version: 16.1–16.16, 16.18, 16.30, 16.34, 16.37–16.40, 16.45–16.46, 16.48, 16.50–16.51
double-angle formula
cosine: 8.8–8.16, 8.18, 8.45, 11.30
sine: 8.1–8.7, 8.11–8.13, 8.16, 8.45, 11.29, 11.31
tangent: 8.39–8.41, 11.31
equation: see solving equations
equivalent vectors: 14.3–14.4, 14.7–14.11, 14.18, 14.34, 15.36
exact solutions: 9.17, 9.19, 10.3, 10.5–10.6, 10.11
factoring
difference of perfect squares: 10.17, 10.21
greatest common factor: 10.16
(by) grouping: 10.22–10.23
trinomials: 10.18–10.20, 10.26, 10.29, 10.44
force: 16.49–16.52
formula: see identity
function: 9.2
G–H
general distance formula: 2.11–2.12
general solution: 9.16, 10.2, 10.4, 10.7, 10.9–10.10, 10.16, 10.18–10.19, 10.21–10.22, 10.40–10.41, 10.43, 10.45, 11.11–11.12, 11.20–11.22
graphing parametric curves: 17.1–17.3, 17.5–17.6, 17.8–17.9, 17.11, 17.13
graphing polar equations: 17.43–17.50
graphing transformations
horizontal compression: 5.20, 5.32, 5.38, 5.41, 6.5, 6.9, 6.15
horizontal shift: 5.15–5.17, 5.27, 5.33, 5.36–5.37, 5.39–5.41, 6.4, 6.10, 6.20
horizontal stretch: 5.21, 5.34, 5.39–5.40, 6.19
reflection about x-axis: 5.22, 5.24, 5.29, 5.34, 6.10, 6.14, 6.20
reflection about y-axis: 5.23, 5.25, 5.30, 5.38, 6.8
reflection about y = x: 9.4
vertical compression: 5.19, 5.34, 6.9
vertical shift: 5.13–5.14, 5.17, 5.25, 5.28, 5.33, 5.38, 6.5, 6.8, 6.14
vertical stretch: 5.18, 5.24, 5.31, 5.37, 6.3
graphing trigonometric functions
cosecant: 6.16–6.20
cosine: 5.35–5.41, 6.11
cotangent: 6.6–6.10
secant: 6.11–6.15
sine: 5.26–5.34, 6.16
tangent: 6.1–6.5, 6.10
greatest common factor: 10.16
grouping (factoring by): 10.22–10.23
half-angle formula
cosine: 8.22, 8.24, 8.26
sine: 8.23, 8.25, 8.27
tangent: 8.44–8.45, 11.34
head-to-tail technique: see adding vectors (graphically)
height: 12.1–12.12, 12.15, 12.21, 12.28
Heron’s formula: 12.25–12.27, 12.29–12.34, 12.44
horizontal line test: 9.2, 9.5
hypotenuse: 2.1–2.10, 2.13–2.20, 2.22–2.24, 2.26–2.28, 2.42–2.43, 2.45, 3.6–3.7, 3.11–3.14, 3.22
i: see standard unit vector
identity
cofunction: 7.1–7.4, 7.6, 7.11–7.12, 7.17–7.18, 7.40–7.41, 8.16
double-angle: 8.1–8.16, 8.18, 8.39–8.41, 8.45
half-angle: 8.22–8.27, 8.44
negative: 7.13–7.22, 7.33, 8.30
power-reducing: 8.17–8.23, 8.42–8.43
product-to-sum: 8.28–8.31
Pythagorean: 7.23–7.33
reciprocal: 7.5–7.10, 7.12, 7.14–7.15, 7.19–7.20, 7.22, 7.26, 7.30–7.33
simplifying: 7.1–7.4, 7.6–7.12, 7.14–7.15, 7.18, 7.21, 7.26–7.28, 7.30, 7.43, 8.3, 8.13, 8.16, 8.26–8.27, 8.37–8.38, 8.41
sum and difference: 7.34–7.45, 8.2, 8.29, 8.36–8.39
sum-to-product: 8.32–8.35
verifying: 7.16–7.17, 7.19–7.20, 7.22, 7.24–7.25, 7.29, 7.31–7.33, 7.41, 7.44, 8.2, 8.6–8.7, 8.9, 8.11, 8.14, 8.18, 8.21–8.23, 8.29, 8.31, 8.35, 8.39, 8.42
imaginary number: 18.1, 18.5
initial point: 14.1–14.14, 14.16, 14.18
initial side: 1.6–1.8
interpolation: 2.32–2.36
interval notation: 5.1–5.2, 5.6–5.7
inverse
functions: 9.1–9.4
trigonometric functions: 2.40–2.41, 2.43, 2.45, 3.27–3.28, 3.45, 9.5–9.26, 10.4–10.6, 10.11, 10.22–10.23, 10.28–10.30, 10.32, 10.45, 11.12, 11.21, 11.25–11.26, 11.35, 12.43, 13.11, 13.16–13.17, 13.19, 13.21
isosceles triangle: 2.7, 2.13, 3.4, 12.7, 12.15–12.16, 12.28, 12.43
j: see standard unit vector
L–M
law of cosines
formula: 13.13–13.14
SAS: 13.18–13.21, 13.23
SSS: 13.14–13.17, 13.21
law of sines
AAS: 13.2–13.4, 13.8
ambiguous case: 13.9–13.12
ASA: 13.5–13.7
formula: 13.1
SSA: 13.9–13.12, 13.17, 13.19
leg: 2.1–2.10, 2.13–2.28, 2.42–2.45, 3.6–3.7, 3.11–3.14, 3.22
lemniscate: 17.50
length (of an arc): 1.41–1.45
length, signed: 4.3–4.5, 4.30–4.35, 4.37–4.39, 4.41–4.45
limaçon: 17.48
linear trigonometric equation: see simple equation
magnitude: 14.25–14.36, 14.38–14.40, 14.48–14.51, 15.20, 15.24, 15.26–15.28, 15.31, 15.34, 15.38–15.45, 16.7–16.8, 16.49–16.50, 16.52
major arc: 1.45
maximum: 5.3–5.4, 5.8
measure
angle: 1.9–1.17, 1.20–1.30
arc: 1.40
minimum: 5.3–5.4, 5.8
minor arc: 1.45
minutes: 1.18–1.19
modulus: 18.13–18.14, 18.18
multiple-angle equation: 10.34–10.45, 11.8
multiplying
complex numbers: 18.8, 18.11, 18.23, 18.25–18.27, 18.38
vectors: see scalar multiplication or dot product
negative
angles: 1.17, 1.26, 1.28
identities: 7.13–7.22, 7.33, 8.30
notation
interval: 5.1–5.2, 5.6–5.7
set: 5.1–5.2, 5.6–5.7
one-to-one function: 9.2
opposite
leg: 2.15–2.17, 2.19, 2.23, 2.42, 2.44–2.45
vector: 14.5, 14.15, 15.7, 15.9–15.11
orthogonal: 16.31–16.40, 16.42, 16.47
parallel lines: 1.38
parametric equations: 17.1–17.14
perimeter
sector: 12.37, 12.42
triangle: 13.3
period: 5.5, 5.9, 5.12, 5.32, 5.41, 6.2, 6.5–6.6, 6.11
periodic functions: 5.1–5.41, 6.1–6.20
perpendicular: 12.4–12.12, 13.3, 16.31
plotting vectors: 14.1, 14.6, 14.14, 14.16, 14.22–14.23, 16.19, 16.32, 16.47
polar
angle: see angular coordinate
axis: 17.16
coordinates: 17.15–17.34, 17.37–17.41
equations: 17.35–17.36, 17.42–17.50
pole: 17.15
power-reducing formula
cosine: 8.17, 8.19–8.22, 8.42
sine: 8.17–8.18, 8.21, 8.23, 8.42
tangent: 8.42–8.43
product-to-sum formula: 8.28–8.31
projection (of a vector): 16.42–16.48, 16.50, 16.52
proportion: 2.33, 2.35–2.36
Pythagorean identity: 7.23–7.33, 8.6–8.7, 8.10, 8.18, 8.21, 8.41, 11.14–11.23, 11.25–11.26, 11.28, 11.33–11.34
Pythagorean theorem: 2.1–2.10, 2.13–2.14, 2.24, 2.26, 3.2, 7.45, 8.4–8.5, 12.5, 12.28, 12.33
Q–R
quadrantal: 3.36
quadratic equation: 10.16–10.19, 10.20, 10.24–10.32, 10.44–10.45
quadratic formula: 10.24–10.25, 10.27–10.28, 10.30–10.32, 10.45, 11.21, 11.35
radial coordinate: 17.15, 17.43–17.44
radian: 1.11–1.14, 1.17
radius: 1.41–1.45, 12.35–12.45, 17.15, 17.43–17.44
range: 5.2, 5.7, 5.10, 6.2, 6.7, 6.13, 6.18, 9.8, 9.11, 9.14
rational equation: 11.7–11.13, 11.27, 11.31, 11.34–11.35
rationalizing the denominator: 3.3, 3.7, 4.31–4.32, 4.34–4.35, 4.38–4.39, 4.43–4.45, 14.40
real part of a complex number: 18.1
reciprocal: 2.21–2.22, 2.24, 2.26, 3.30, 6.12, 6.17
reciprocal identity: 7.5–7.10, 7.12, 7.14–7.15, 7.19–7.20, 7.22, 7.26, 7.30–7.33
rectangle: 12.1
rectangular form: 17.4, 17.7, 17.10, 17.12, 17.14, 17.30–17.42, 17.46, 18.1–18.17, 18.21–18.22, 18.24–18.25, 18.29–18.30, 18.34
reference angle: 4.1–4.5, 4.30, 4.33, 4.37, 4.44, 7.45, 8.4–8.5, 13.12
reflection: see graphing transformations
restricted domain and range: 9.5, 9.9, 9.11–9.12, 9.14, 9.20–9.26
resultant vector: 15.1–15.11, 15.14
revolution: 1.9, 1.14–1.15
right angle: 1.14
30°–60°–90° triangle: 1.34, 3.10–3.21
45°–45°–90° triangle: 2.7, 3.1–3.9
adjacent leg: 2.15–2.16, 2.18–2.23, 2.43–2.44, 3.14
cosecant: 2.22, 2.24
cosine: 2.18, 2.20, 2.26–2.28, 2.43, 12.12
cotangent: 2.21, 2.25, 3.42, 4.29, 4.38, 4.42, 4.45
hypotenuse: 2.1–2.10, 2.13–2.20, 2.22–2.24, 2.26–2.28, 2.42–2.43, 2.45, 3.6–3.7, 3.11–3.14, 3.22
isosceles: 2.7, 3.4
leg: 2.1–2.10, 2.13–2.28, 2.42–2.45, 3.6–3.7, 3.11–3.14, 3.22
opposite leg: 2.15–2.17, 2.19, 2.23, 2.42, 2.44–2.45
Pythagorean theorem: 2.1–2.10, 2.13–2.14, 2.24, 2.26, 3.2, 7.45, 8.4–8.5, 12.5, 12.28, 12.33
secant: 2.22, 2.26, 4.35, 4.44
sine: 2.17, 2.20, 2.24, 2.27–2.28, 2.42, 2.45, 12.43
tangent: 2.19, 2.21, 2.23, 2.28, 2.44, 2.46, 12.11, 14.44–14.45
terminal side: 1.6–1.8, 1.15–1.17, 3.34, 3.36
roots of complex numbers: 18.40–18.45
rose curve: 17.49
S
same-side interior angles: 1.38
scalar multiplication: 14.46–14.48, 14.50–14.51, 15.21–15.36, 16.3–16.4, 16.12–16.16
secant: 2.22, 2.26, 3.30, 4.35, 4.44, 6.11–6.15
seconds: 1.18–1.19
sector
area: 12.35, 12.38–12.39, 12.41, 12.43, 12.45
perimeter: 12.37, 12.42
semicircle: 1.45
semiperimeter: 12.25–12.27, 12.29–12.32, 12.34, 12.44, 13.24
set notation: 5.1–5.2, 5.6–5.7
shift: see graphing transformations
side: 1.1
signed length: 4.3–4.5, 4.30–4.35, 4.37–4.39, 4.41–4.45
simple equation: 9.15–9.19, 10.1–10.11, 10.33–10.45
simplifying identities: 7.1–7.4, 7.6–7.12, 7.14–7.15, 7.18, 7.21, 7.26–7.28, 7.30, 7.43, 8.3, 8.13, 8.16, 8.26–8.27, 8.37–8.38, 8.41
sine: 2.17, 2.20, 2.24, 2.27–2.28, 2.42, 2.45, 3.22, 3.25, 3.27, 3.32, 3.37–3.38, 3.41, 3.45, 4.3, 4.26, 4.31, 4.33, 4.44, 5.26–5.34, 6.16, 12.43, 15.37–15.44
solution
exact: 9.17, 9.19, 10.3, 10.5–10.6, 10.11
general: 9.16, 10.2, 10.4, 10.7, 10.9–10.10, 10.16, 10.18–10.19, 10.21–10.22, 10.40–10.41, 10.43, 10.45, 11.11–11.12, 11.20–11.22
(on an) interval: 9.15, 9.18, 10.1, 10.8, 10.14, 10.17, 10.20, 10.23, 10.27–10.30, 10.32–10.39, 10.42–10.44, 11.1–11.10, 11.13–11.19, 11.23–11.35
solving equations
(involving) double-angle identities: 11.29–11.31
(involving) half-angle formulas: 11.34
multiple angles: 10.34–10.45, 11.8
(using) Pythagorean identities: 11.14–11.23, 11.25–11.26, 11.28, 11.33–11.34
quadratic: 10.16–10.20, 10.24–10.32, 10.44–10.45
rational: 11.7–11.13, 11.27, 11.31, 11.34–11.35
simple: 9.15–9.19, 10.1–10.11, 10.33–10.45
(using) square roots: 11.2–11.7, 11.10, 11.14–11.15, 11.20
(by) squaring both sides: 11.23–11.26, 11.28
(involving) sum and difference formulas: 11.32–11.33, 11.35
(using) trigonometric identities: 11.4–11.23, 11.25–11.26, 11.28–11.35
zero-product property: 11.1, 11.3, 11.6, 11.10–11.11, 11.16–11.19, 11.22–11.23, 11.25, 11.29–11.34
square root: 11.2–11.7, 11.10, 11.14–11.15, 11.20, 18.41–18.42
standard position: 1.3–1.8, 1.14, 3.5–3.8, 3.17–3.22
standard unit vector: 14.41–14.43, 15.8–15.9
straight angle: 1.35–1.37
stretch: see graphing transformations
subtend: 1.12, 1.40
subtracting
complex numbers: 18.7, 18.10
vectors (algebraically): 15.13, 15.16, 15.18–15.19, 15.30–15.35
vectors (graphically): 15.7, 15.9–15.11
sum and difference formula
cosine: 7.37–7.39, 7.41, 7.43, 8.9, 8.29, 11.32
sine: 7.34–7.36, 7.40, 7.43–7.45, 8.2, 11.33
tangent: 8.36–8.39, 11.35
sum-to-product formula: 8.32–8.35
supplementary angles: 1.35–1.39
T
tangent: 2.19, 2.21, 2.23, 2.28, 2.44, 3.29, 3.33, 3.44, 4.5, 4.30, 4.34, 4.41, 4.45, 6.1–6.5, 6.10, 12.11, 14.44–14.45, 15.37
terminal point: 14.1–14.14, 14.16, 14.18
terminal side: 1.6–1.8, 1.15–1.17, 3.34, 3.36, 4.36, 4.40, 4.44
transformation: see graphing transformations
transversal: 1.38
triangle
area: see area of a triangle
right: 1.34
sides: 1.1
vertex: 1.1, 1.3
trigonometric form of a complex number: 18.16, 18.18–18.23, 18.26–18.28, 18.31–18.33, 18.35–18.45
trigonometric function
cosecant: 2.22, 2.24, 3.43, 4.39, 4.44, 6.16–6.20
cosine: 2.18, 2.20, 2.26–2.28, 2.43, 3.14, 3.22, 3.24, 3.26, 3.28, 3.30, 3.32, 3.35, 3.39–3.40, 4.4, 4.28, 4.32, 4.37, 4.43, 5.35–5.41, 6.11, 12.12, 15.37–15.44
cotangent: 2.21, 2.25, 3.42, 6.6–6.10
inverse: 9.5–9.26
outside of the unit circle: 4.26, 4.28–4.45, 7.45
secant: 2.22, 2.26, 3.30, 6.11–6.15
sine: 2.17, 2.20, 2.24, 2.27–2.28, 2.42, 2.45, 3.22, 3.25, 3.27, 3.32, 3.37–3.38, 3.41, 3.45, 4.3, 4.26, 4.31, 4.33, 4.44, 5.26–5.34, 6.16, 12.43, 15.37–15.44
tangent: 2.19, 2.21, 2.23, 2.28, 2.44, 2.46, 3.29, 3.33, 3.44, 4.5, 4.30, 4.34, 4.41, 4.45, 6.1–6.5, 6.10, 12.11, 14.44–14.45, 15.37
trigonometric identity: see identity
trigonometric tables: 2.29–2.36
trigonometric triangle area formula: 12.13–12.14, 12.16–12.20, 12.22–12.27, 12.29–12.34
U–V
undefined: 5.10
unit circle: 3.8, 3.18–3.19, 3.23–3.45, 4.26, 4.28–4.29, 5.26, 5.35
unit vector: 14.37–14.43, 14.48, 14.50–14.51, 15.31, 16.28–16.30
vector
adding algebraically: 15.12, 15.15, 15.17, 15.20, 15.29, 16.48
adding graphically: 15.1–15.11, 15.14, 15.27, 16.41, 16.44
angle between vectors: 16.19–16.27, 16.29, 16.36
component form: 14.12–14.24, 14.31–14.32, 15.19–15.20, 15.38–15.44
direction angle: 14.44–14.48, 14.50–14.51, 15.37–15.44
dot product: 16.1–16.18, 16.27, 16.29–16.30, 16.34–16.40, 16.45–16.46, 16.48, 16.50–16.51
equivalent: 14.3–14.4, 14.7–14.11, 14.18, 14.34, 15.36
force: 16.49–16.52
head-to-tail technique: see adding vectors (graphically)
initial point: 14.1–14.14, 14.16, 14.18
magnitude: 14.25–14.36, 14.38–14.40, 14.48–14.51, 15.20, 15.24, 15.26–15.28, 15.31, 15.34, 15.38–15.45, 16.7–16.8, 16.49–16.50, 16.52
multiplying: see scalar multiplication or dot product
naming: 14.2
opposite: 14.5, 14.15, 15.7, 15.9–15.11
orthogonal: 16.31–16.40, 16.42, 16.47
plotting: 14.1, 14.6, 14.14, 14.16, 14.22–14.23, 16.19, 16.32, 16.47
projection: 16.42–16.48, 16.50, 16.52
resultant: 15.1–15.11, 15.14
scalar multiplication: 14.46–14.48, 14.50–14.51, 15.21–15.36, 16.3–16.4, 16.12–16.16
standard unit vectors: 14.41–14.43, 15.8–15.9
subtracting algebraically: 15.13, 15.16, 15.18–15.19, 15.30–15.35
subtracting graphically: 15.7, 15.9–15.11
terminal point: 14.1–14.14, 14.16, 14.18
unit vector: 14.37–14.43, 14.48, 14.50–14.51, 15.31, 16.28–16.30
work: 16.49–16.52
zero vector: 16.35
verifying identities: 7.16–7.17, 7.19–7.20, 7.22, 7.24–7.25, 7.29, 7.31–7.33, 7.41, 7.44, 8.2, 8.6–8.7, 8.9, 8.11, 8.14, 8.18, 8.21–8.23, 8.29, 8.31, 8.35, 8.39, 8.42
vertex: 1.1, 1.3
vertical asymptote: see asymptote
vertical line test: 9.2
W–X–Y–Z
work: 16.49–16.52
y-symmetric: 5.38
zero-product property: 10.12–10.23, 10.26, 10.29, 10.44, 11.1, 11.3, 11.6, 11.10–11.11, 11.16–11.19, 11.22–11.23, 11.25, 11.29–11.34
zero vector: 16.35