, R E F E R E N C E PA G E 1
ALGEBRA GEOMETRY
Cut here and keep for reference
Arithmetic Operations Geometric Formulas
a c ad bc Formulas for area A, circumference C, and volume V:
a共b c兲 苷 ab ac 苷
b d bd
Triangle Circle Sector of Circle
a
A 苷 12 bh A 苷 r 2 A 苷 12 r 2
ac a c b a d ad
苷 苷 苷
b b b c b c bc 苷 12 ab sin C 苷 2 r s 苷 r 共 in radians兲
d
a
Exponents and Radicals h r s
m ¨ r
x ¨
x m x n 苷 x mn 苷 x mn b
xn r
1
共x 兲 苷 x
m n mn
xn 苷 n
x
共xy兲n 苷 x n y n 冉冊 x
y
n
苷
xn
yn
Sphere
V 苷 43 r 3
Cylinder
V 苷 r 2h
Cone
V 苷 13 r 2h
x 1兾n 苷 s
n
x x m兾n 苷 s
n
x m 苷 (s
n
x )m A 苷 4 r 2 A 苷 rsr 2 h 2
n
s xy 苷 s
n n
xs y 冑 n x
y
n
s
苷 n
sy
x r
r h
h
Factoring Special Polynomials
r
x 2 y 2 苷 共x y兲共x y兲
x 3 y 3 苷 共x y兲共x 2 xy y 2兲
x 3 y 3 苷 共x y兲共x 2 xy y 2兲
Distance and Midpoint Formulas
Binomial Theorem
Distance between P1共x1, y1兲 and P2共x 2, y2兲:
共x y兲2 苷 x 2 2xy y 2 共x y兲2 苷 x 2 2xy y 2
共x y兲3 苷 x 3 3x 2 y 3xy 2 y 3 d 苷 s共x 2 x1兲2 共 y2 y1兲2
共x y兲3 苷 x 3 3x 2 y 3xy 2 y 3
共x y兲n 苷 x n nx n1y
n共n 1兲 n2 2
2
x y
Midpoint of P1 P2 : 冉 x1 x 2 y1 y2
2
,
2
冊
冉冊 n nk k
k
x y nxy n1 y n
冉冊
Lines
n n共n 1兲 共n k 1兲
where 苷 Slope of line through P1共x1, y1兲 and P2共x 2, y2兲:
k 1ⴢ2ⴢ3ⴢ ⴢk
y2 y1
Quadratic Formula m苷
x 2 x1
b sb 2 4ac
If ax 2 bx c 苷 0, then x 苷 .
2a Point-slope equation of line through P1共x1, y1兲 with slope m:
Inequalities and Absolute Value y y1 苷 m共x x1兲
If a b and b c, then a c.
Slope-intercept equation of line with slope m and y-intercept b:
If a b, then a c b c.
If a b and c 0, then ca cb. y 苷 mx b
If a b and c 0, then ca cb.
If a 0, then
Circles
ⱍxⱍ 苷 a means x 苷 a or x 苷 a
Equation of the circle with center 共h, k兲 and radius r:
ⱍxⱍ a means a x a
ⱍxⱍ a means xa or x a 共x h兲2 共 y k兲2 苷 r 2
Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
, R E F E R E N C E PA G E 2
TRIGONOMETRY
Angle Measurement Fundamental Identities
radians 苷 180⬚ 1 1
s csc 苷 sec 苷
r sin cos
180⬚
1⬚ 苷 rad 1 rad 苷 ¨
180 sin cos
r tan 苷 cot 苷
s 苷 r cos sin
共 in radians兲 1
cot 苷 sin 2 ⫹ cos 2 苷 1
tan
Right Angle Trigonometry 1 ⫹ tan 2 苷 sec 2 1 ⫹ cot 2 苷 csc 2
opp hyp
sin 苷 csc 苷 sin共⫺兲 苷 ⫺sin cos共⫺兲 苷 cos
hyp opp hyp
冉 冊
opp
cos 苷
adj
sec 苷
hyp ¨
tan共⫺兲 苷 ⫺tan sin ⫺ 苷 cos
hyp adj 2
adj
冉 冊 冉 冊
opp adj
tan 苷 cot 苷
adj opp cos ⫺ 苷 sin tan ⫺ 苷 cot
2 2
Trigonometric Functions
The Law of Sines B
y r y
sin 苷 csc 苷 sin A sin B sin C
r y 苷 苷
a
(x, y) a b c
x r r
cos 苷 sec 苷 C
r x c
y x ¨
tan 苷 cot 苷 The Law of Cosines
x
x y b
a 2 苷 b 2 ⫹ c 2 ⫺ 2bc cos A
Graphs of Trigonometric Functions b 2 苷 a 2 ⫹ c 2 ⫺ 2ac cos B
y y y A
y=tan x c 2 苷 a 2 ⫹ b 2 ⫺ 2ab cos C
y=sin x y=cos x
1 1
π 2π 2π Addition and Subtraction Formulas
x π 2π x π x sin共x ⫹ y兲 苷 sin x cos y ⫹ cos x sin y
_1 _1 sin共x ⫺ y兲 苷 sin x cos y ⫺ cos x sin y
cos共x ⫹ y兲 苷 cos x cos y ⫺ sin x sin y
y y=csc x y y=sec x y y=cot x cos共x ⫺ y兲 苷 cos x cos y ⫹ sin x sin y
tan x ⫹ tan y
1 1 tan共x ⫹ y兲 苷
1 ⫺ tan x tan y
tan x ⫺ tan y
π 2π x π 2π x π 2π x tan共x ⫺ y兲 苷
1 ⫹ tan x tan y
_1 _1
Double-Angle Formulas
sin 2x 苷 2 sin x cos x
Trigonometric Functions of Important Angles cos 2x 苷 cos 2x ⫺ sin 2x 苷 2 cos 2x ⫺ 1 苷 1 ⫺ 2 sin 2x
radians sin cos tan 2 tan x
tan 2x 苷
0⬚ 0 0 1 0 1 ⫺ tan2x
30⬚ 兾6 1兾2 s3兾2 s3兾3
45⬚ 兾4 s2兾2 s2兾2 1 Half-Angle Formulas
60⬚ 兾3 s3兾2 1兾2 s3 1 ⫺ cos 2x 1 ⫹ cos 2x
sin 2x 苷 cos 2x 苷
90⬚ 兾2 1 0 — 2 2
Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
, This is an electronic version of the print textbook. Due to electronic rights
restrictions, some third party content may be suppressed. Editorial
review has deemed that any suppressed content does not materially
affect the overall learning experience. The publisher reserves the
right to remove content from this title at any time if subsequent
rights restrictions require it. For valuable information on pricing, previous
editions, changes to current editions, and alternate formats, please visit
www.cengage.com/highered to search by ISBN#, author, title, or keyword
for materials in your areas of interest.
Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
52609_00_fm_pi-pxxvi.indd ii 2/1/10 11:37:43
ALGEBRA GEOMETRY
Cut here and keep for reference
Arithmetic Operations Geometric Formulas
a c ad bc Formulas for area A, circumference C, and volume V:
a共b c兲 苷 ab ac 苷
b d bd
Triangle Circle Sector of Circle
a
A 苷 12 bh A 苷 r 2 A 苷 12 r 2
ac a c b a d ad
苷 苷 苷
b b b c b c bc 苷 12 ab sin C 苷 2 r s 苷 r 共 in radians兲
d
a
Exponents and Radicals h r s
m ¨ r
x ¨
x m x n 苷 x mn 苷 x mn b
xn r
1
共x 兲 苷 x
m n mn
xn 苷 n
x
共xy兲n 苷 x n y n 冉冊 x
y
n
苷
xn
yn
Sphere
V 苷 43 r 3
Cylinder
V 苷 r 2h
Cone
V 苷 13 r 2h
x 1兾n 苷 s
n
x x m兾n 苷 s
n
x m 苷 (s
n
x )m A 苷 4 r 2 A 苷 rsr 2 h 2
n
s xy 苷 s
n n
xs y 冑 n x
y
n
s
苷 n
sy
x r
r h
h
Factoring Special Polynomials
r
x 2 y 2 苷 共x y兲共x y兲
x 3 y 3 苷 共x y兲共x 2 xy y 2兲
x 3 y 3 苷 共x y兲共x 2 xy y 2兲
Distance and Midpoint Formulas
Binomial Theorem
Distance between P1共x1, y1兲 and P2共x 2, y2兲:
共x y兲2 苷 x 2 2xy y 2 共x y兲2 苷 x 2 2xy y 2
共x y兲3 苷 x 3 3x 2 y 3xy 2 y 3 d 苷 s共x 2 x1兲2 共 y2 y1兲2
共x y兲3 苷 x 3 3x 2 y 3xy 2 y 3
共x y兲n 苷 x n nx n1y
n共n 1兲 n2 2
2
x y
Midpoint of P1 P2 : 冉 x1 x 2 y1 y2
2
,
2
冊
冉冊 n nk k
k
x y nxy n1 y n
冉冊
Lines
n n共n 1兲 共n k 1兲
where 苷 Slope of line through P1共x1, y1兲 and P2共x 2, y2兲:
k 1ⴢ2ⴢ3ⴢ ⴢk
y2 y1
Quadratic Formula m苷
x 2 x1
b sb 2 4ac
If ax 2 bx c 苷 0, then x 苷 .
2a Point-slope equation of line through P1共x1, y1兲 with slope m:
Inequalities and Absolute Value y y1 苷 m共x x1兲
If a b and b c, then a c.
Slope-intercept equation of line with slope m and y-intercept b:
If a b, then a c b c.
If a b and c 0, then ca cb. y 苷 mx b
If a b and c 0, then ca cb.
If a 0, then
Circles
ⱍxⱍ 苷 a means x 苷 a or x 苷 a
Equation of the circle with center 共h, k兲 and radius r:
ⱍxⱍ a means a x a
ⱍxⱍ a means xa or x a 共x h兲2 共 y k兲2 苷 r 2
Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
, R E F E R E N C E PA G E 2
TRIGONOMETRY
Angle Measurement Fundamental Identities
radians 苷 180⬚ 1 1
s csc 苷 sec 苷
r sin cos
180⬚
1⬚ 苷 rad 1 rad 苷 ¨
180 sin cos
r tan 苷 cot 苷
s 苷 r cos sin
共 in radians兲 1
cot 苷 sin 2 ⫹ cos 2 苷 1
tan
Right Angle Trigonometry 1 ⫹ tan 2 苷 sec 2 1 ⫹ cot 2 苷 csc 2
opp hyp
sin 苷 csc 苷 sin共⫺兲 苷 ⫺sin cos共⫺兲 苷 cos
hyp opp hyp
冉 冊
opp
cos 苷
adj
sec 苷
hyp ¨
tan共⫺兲 苷 ⫺tan sin ⫺ 苷 cos
hyp adj 2
adj
冉 冊 冉 冊
opp adj
tan 苷 cot 苷
adj opp cos ⫺ 苷 sin tan ⫺ 苷 cot
2 2
Trigonometric Functions
The Law of Sines B
y r y
sin 苷 csc 苷 sin A sin B sin C
r y 苷 苷
a
(x, y) a b c
x r r
cos 苷 sec 苷 C
r x c
y x ¨
tan 苷 cot 苷 The Law of Cosines
x
x y b
a 2 苷 b 2 ⫹ c 2 ⫺ 2bc cos A
Graphs of Trigonometric Functions b 2 苷 a 2 ⫹ c 2 ⫺ 2ac cos B
y y y A
y=tan x c 2 苷 a 2 ⫹ b 2 ⫺ 2ab cos C
y=sin x y=cos x
1 1
π 2π 2π Addition and Subtraction Formulas
x π 2π x π x sin共x ⫹ y兲 苷 sin x cos y ⫹ cos x sin y
_1 _1 sin共x ⫺ y兲 苷 sin x cos y ⫺ cos x sin y
cos共x ⫹ y兲 苷 cos x cos y ⫺ sin x sin y
y y=csc x y y=sec x y y=cot x cos共x ⫺ y兲 苷 cos x cos y ⫹ sin x sin y
tan x ⫹ tan y
1 1 tan共x ⫹ y兲 苷
1 ⫺ tan x tan y
tan x ⫺ tan y
π 2π x π 2π x π 2π x tan共x ⫺ y兲 苷
1 ⫹ tan x tan y
_1 _1
Double-Angle Formulas
sin 2x 苷 2 sin x cos x
Trigonometric Functions of Important Angles cos 2x 苷 cos 2x ⫺ sin 2x 苷 2 cos 2x ⫺ 1 苷 1 ⫺ 2 sin 2x
radians sin cos tan 2 tan x
tan 2x 苷
0⬚ 0 0 1 0 1 ⫺ tan2x
30⬚ 兾6 1兾2 s3兾2 s3兾3
45⬚ 兾4 s2兾2 s2兾2 1 Half-Angle Formulas
60⬚ 兾3 s3兾2 1兾2 s3 1 ⫺ cos 2x 1 ⫹ cos 2x
sin 2x 苷 cos 2x 苷
90⬚ 兾2 1 0 — 2 2
Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
, This is an electronic version of the print textbook. Due to electronic rights
restrictions, some third party content may be suppressed. Editorial
review has deemed that any suppressed content does not materially
affect the overall learning experience. The publisher reserves the
right to remove content from this title at any time if subsequent
rights restrictions require it. For valuable information on pricing, previous
editions, changes to current editions, and alternate formats, please visit
www.cengage.com/highered to search by ISBN#, author, title, or keyword
for materials in your areas of interest.
Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
52609_00_fm_pi-pxxvi.indd ii 2/1/10 11:37:43
