R E F E R E N C E PA G E S
Cut here and keep for reference
ALGEBRA
GEOMETRY
Arithmetic Operations
Geometric Formulas
a
c
ad ⫹ bc
⫹ 苷
b
d
bd
a
b
a
d
ad
苷 ⫻ 苷
c
b
c
bc
d
a共b ⫹ c兲 苷 ab ⫹ ac
a⫹c
a
c
苷 ⫹
b
b
b
Formulas for area A, circumference C, and volume V:
Triangle
Circle
Sector of Circle
A 苷 12 bh
A 苷 ␲r 2
A 苷 12 r 2␪
C 苷 2␲ r
s 苷 r ␪ 共␪ in radians兲
苷 12 ab sin ␪
a
Exponents and Radicals
m
x
苷 x m⫺n
xn
1
x⫺n 苷 n
x
x m x n 苷 x m⫹n
共x 兲 苷 x
m n
mn
冉冊
x
y
共xy兲n 苷 x n y n
n
苷
冑
n
n
n
n
xy 苷 s
xs
y
s
¨
r
xn
yn
Sphere
Cylinder
Cone
V 苷 43 ␲ r 3
V 苷 ␲ r 2h
V 苷 13 ␲ r 2h
A 苷 4␲ r 2
A 苷 ␲ rsr 2 ⫹ h 2
n
x
x
s
苷 n
y
sy
r
r
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
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3 苷 x 3 ⫺ 3x 2 y ⫹ 3xy 2 ⫺ y 3
共x ⫹ y兲n 苷 x n ⫹ nx n⫺1y ⫹
⫹ ⭈⭈⭈ ⫹
冉冊
n共n ⫺ 1兲 n⫺2 2
x y
2
Midpoint of P1 P2 :
冉冊
n n⫺k k
x y ⫹ ⭈ ⭈ ⭈ ⫹ nxy n⫺1 ⫹ y n
k
冉
x1 ⫹ x 2 y1 ⫹ y2
,
2
2
冊
Lines
n
n共n ⫺ 1兲 ⭈ ⭈ ⭈ 共n ⫺ k ⫹ 1兲
苷
where
k
1 ⴢ 2 ⴢ 3 ⴢ ⭈⭈⭈ ⴢ k
Slope of line through P1共x1, y1兲 and P2共x 2, y2兲:
m苷
Quadratic Formula
If ax 2 ⫹ bx ⫹ c 苷 0, then x 苷
⫺b ⫾ sb 2 ⫺ 4ac
.
2a
y2 ⫺ y1
x 2 ⫺ x1
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
ⱍxⱍ 苷 a
ⱍxⱍ ⬍ a
ⱍxⱍ ⬎ a
means
x 苷 a or
Circles
x 苷 ⫺a
Equation of the circle with center 共h, k兲 and radius r:
means ⫺a ⬍ x ⬍ a
means
x ⬎ a or
h
h
Factoring Special Polynomials
共x ⫹ y兲2 苷 x 2 ⫹ 2xy ⫹ y 2
s
r
b
n
n
x m兾n 苷 s
x m 苷 (s
x )m
n
x 1兾n 苷 s
x
r
h
¨
共x ⫺ h兲2 ⫹ 共 y ⫺ k兲2 苷 r 2
x ⬍ ⫺a
1
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R E F E R E N C E PA G E S
TRIGONOMETRY
Angle Measurement
Fundamental Identities
␲ radians 苷 180⬚
csc ␪ 苷
1
sin ␪
sec ␪ 苷
1
cos ␪
tan ␪ 苷
sin ␪
cos ␪
cot ␪ 苷
cos ␪
sin ␪
共␪ in radians兲
cot ␪ 苷
1
tan ␪
sin 2␪ ⫹ cos 2␪ 苷 1
Right Angle Trigonometry
1 ⫹ tan 2␪ 苷 sec 2␪
1 ⫹ cot 2␪ 苷 csc 2␪
sin共⫺␪兲 苷 ⫺sin ␪
cos共⫺␪兲 苷 cos ␪
tan共⫺␪兲 苷 ⫺tan ␪
sin
␲
⫺ ␪ 苷 cos ␪
2
tan
␲
⫺ ␪ 苷 cot ␪
2
1⬚ 苷
␲
rad
180
1 rad 苷
180⬚
␲
¨
r
s 苷 r␪
sin ␪ 苷
cos ␪ 苷
tan ␪ 苷
opp
hyp
csc ␪ 苷
adj
hyp
sec ␪ 苷
opp
adj
cot ␪ 苷
s
r
hyp
opp
hyp
hyp
adj
冉 冊
冉 冊
opp
¨
adj
冉 冊
adj
opp
cos
␲
⫺ ␪ 苷 sin ␪
2
Trigonometric Functions
sin ␪ 苷
y
r
csc ␪ 苷
r
y
cos ␪ 苷
x
r
sec ␪ 苷
r
x
tan ␪ 苷
y
x
cot ␪ 苷
x
y
The Law of Sines
y
sin A
sin B
sin C
苷
苷
a
b
c
(x, y)
C
c
¨
The Law of Cosines
x
b 2 苷 a 2 ⫹ c 2 ⫺ 2ac cos B
y
A
c 2 苷 a 2 ⫹ b 2 ⫺ 2ab cos C
y=tan x
y=cos x
1
1
π
b
a 2 苷 b 2 ⫹ c 2 ⫺ 2bc cos A
y
y=sin x
a
r
Graphs of Trigonometric Functions
y
B
2π
Addition and Subtraction Formulas
2π
x
_1
π
2π x
π
sin共x ⫹ y兲 苷 sin x cos y ⫹ cos x sin y
x
sin共x ⫺ y兲 苷 sin x cos y ⫺ cos x sin y
_1
cos共x ⫹ y兲 苷 cos x cos y ⫺ sin x sin y
y
y
y=csc x
y
y=sec x
cos共x ⫺ y兲 苷 cos x cos y ⫹ sin x sin y
y=cot x
1
1
π
2π x
π
2π x
π
2π x
tan共x ⫹ y兲 苷
tan x ⫹ tan y
1 ⫺ tan x tan y
tan共x ⫺ y兲 苷
tan x ⫺ tan y
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 ␪
0⬚
30⬚
45⬚
60⬚
90⬚
0
␲兾6
␲兾4
␲兾3
␲兾2
0
1兾2
s2兾2
s3兾2
1
1
s3兾2
s2兾2
1兾2
0
0
s3兾3
1
s3
—
tan 2x 苷
2 tan x
1 ⫺ tan2x
Half-Angle Formulas
sin 2x 苷
2
1 ⫺ cos 2x
2
cos 2x 苷
1 ⫹ cos 2x
2