MAT 1320 Chapter 1-5: Calculus Early Transcendentals - 7E
11 May 2018
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Department
Course
Professor
REFERENCE PAGE 1
ALGEBRA
Arithmetic Operations
Exponents and Radicals
Factoring Special Polynomials
Binomial Theorem
where
Quadratic Formula
If , then .
Inequalities and Absolute Value
If and , then .
If , then .
If and , then .
If and , then .
If , then
means or
means
means or
GEOMETRY
Geometric Formulas
Formulas for area A, circumference C, and volume V:
Triangle Circle Sector of Circle
Sphere Cylinder Cone
Distance and Midpoint Formulas
Distance between and :
Midpoint of :
Lines
Slope of line through and :
Point-slope equation of line through with slope m:
Slope-intercept equation of line with slope mand y-intercept b:
Circles
Equation of the circle with center and radius r:
a
b
c
d
苷a
bd
c苷ad
bc
A苷
rsr2h2
共xh兲2共yk兲2苷r2
共h, k兲
y苷mx b
yy1苷m共xx1兲
P1共x1, y1兲
m苷y2y1
x2x1
P2共x2, y2兲P1共x1, y1兲
冉x1x2
2, y1y2
2冊
P1P2
d苷s共x2x1兲2共y2y1兲2
P2共x2, y2兲P1共x1, y1兲
h
r
r
h
r
A苷4
r2
V苷1
3
r2hV 苷
r2hV 苷4
3
r3
r
r
rs
¨
¨
ah
b
s苷r
共
in radians兲C苷2
r苷1
2ab sin
A苷1
2r2
A苷
r2
A苷1
2bh
xax a
ⱍ
x
ⱍ
a
axa
ⱍ
x
ⱍ
a
x苷ax 苷a
ⱍ
x
ⱍ
苷a
a0
ca cbc 0ab
ca cbc 0ab
acbca b
acb ca b
x苷bsb24ac
2a
ax2bx c苷0
冉n
k冊苷n共n1兲共nk1兲
1ⴢ2ⴢ3ⴢⴢk
冉n
k冊xnkyknxyn1yn
共xy兲n苷xnnxn1yn共n1兲
2 xn2y2
共xy兲3苷x33x2y3xy2y3
共xy兲3苷x33x2y3xy2y3
共xy兲2苷x22xy y2
共xy兲2苷x22xy y2
x3y3苷共xy兲共x2xy y2兲
x3y3苷共xy兲共x2xy y2兲
x2y2苷共xy兲共xy兲
n
冑x
y苷s
nx
s
ny
s
nxy 苷s
nxs
ny
xm兾n苷s
nxm苷
(
s
nx
)
m
x1兾n苷s
nx
冉x
y冊n
苷xn
yn
共xy兲n苷xnyn
xn苷1
xn
共xm兲n苷xmn
xm
xn苷xmn
xmxn苷xmn
ac
b苷a
bc
b
a
bc
d苷ad bc
bd
a共bc兲苷ab ac
Cut here and keep for reference
97909_FrontEP_FrontEP_pF2_RefPage1-2_97909_FrontEP_FrontEP_pF2_RefPage1-2 9/24/10 5:36 PM Page 1
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.
Angle Measurement
Right Angle Trigonometry
Trigonometric Functions
Graphs of Trigonometric Functions
Trigonometric Functions of Important Angles
radians
0010
1
10—
兾290⬚
s3
1兾2
s3兾2
兾360⬚
s2兾2
s2兾2
兾445⬚
s3兾3
s3兾21兾2
兾630⬚
0⬚
tan
cos
sin
π 2π x
yy=cotx
x
1
_1
y
π 2π
y=secx
y=cscx
π 2π x
y
1
_1
x
y
π
2π
y=tanx
y=cosx
π 2π x
y
1
_1
y=sinx
x
y
1
_1
π 2π
cot
苷x
y
tan
苷y
x
sec
苷r
x
cos
苷x
r
(x,y)
r
¨x
y
csc
苷r
y
sin
苷y
r
cot
苷adj
opp
tan
苷opp
adj
sec
苷hyp
adj
cos
苷adj
hyp ¨
opp
adj
hyp
csc
苷hyp
opp
sin
苷opp
hyp
共
in radians兲
s苷r
1 rad 苷180⬚
1⬚苷
180 rad
r
r
¨
s
radians 苷180⬚
REFERENCE PAGE 2
TRIGONOMETRY
Fundamental Identities
The Law of Sines
The Law of Cosines
Addition and Subtraction Formulas
Double-Angle Formulas
Half-Angle Formulas
cos2x苷1⫹cos 2x
2
sin2x苷1⫺cos 2x
2
tan 2x苷2 tan x
1⫺tan2x
cos 2x苷cos2x⫺sin2x苷2 cos2x⫺1苷1⫺2 sin2x
sin 2x苷2 sin xcos x
tan共x⫺y兲苷tan x⫺tan y
1⫹tan xtan y
tan共x⫹y兲苷tan x⫹tan y
1⫺tan xtan y
cos共x⫺y兲苷cos xcos y⫹sin xsin y
cos共x⫹y兲苷cos xcos y⫺sin xsin y
sin共x⫺y兲苷sin xcos y⫺cos xsin y
sin共x⫹y兲苷sin xcos y⫹cos xsin y
c2苷a2⫹b2⫺2ab cos C
b2苷a2⫹c2⫺2ac cos B
a2苷b2⫹c2⫺2bc cos A
A
b
c
a
B
C
sin A
a苷sin B
b苷sin C
c
tan冉
2⫺
冊苷cot
cos冉
2⫺
冊苷sin
sin冉
2⫺
冊苷cos
tan共⫺
兲苷⫺tan
cos共⫺
兲苷cos
sin共⫺
兲苷⫺sin
1⫹cot2
苷csc2
1⫹tan2
苷sec2
sin2
⫹cos2
苷1cot
苷1
tan
cot
苷cos
sin
tan
苷sin
cos
sec
苷1
cos
csc
苷1
sin
97909_FrontEP_FrontEP_pF2_RefPage1-2_97909_FrontEP_FrontEP_pF2_RefPage1-2 9/24/10 5:36 PM Page 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.
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MAT 1320 Full Course Notes
Verified Note
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