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  • Topic: Association of Public and Land-Grant Universities, Oak Ridge Associated Universities, North Central Association of Colleges and Schools
  • Pages : 224 (37079 words )
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  • Published : January 25, 2013
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R E F E R E N C E PA G E 1

ALGEBRA
Cut here and keep for reference

GEOMETRY
Geometric Formulas
a b a b c d c d a b ad bd d c ad bc bc Formulas for area A, circumference C, and volume V: Triangle A 1 2 1 2

Arithmetic Operations
ab a b c c a b ab c b ac

Circle A C r2 2 r

Sector of Circle A s
1 2

bh ab sin

r2 in radians

r

Exponents and Radicals
x mx n x
m n

a

h r b ¨

r

s

xm x
mn

n

x xn x

m

¨

xm 1 xn
n

n

r

n

xy x1 n

n

x nyn
n sx

x y xm n
n

xn yn
n sx m

Sphere V 4 r3 3

Cylinder V r 2h

Cone V 1 r 2h 3 A rsr 2 h2

(sx ) m
n

A

4 r2
r r

n sxy

n n sx sy

x y

n sx n sy

Factoring Special Polynomials
x2 x3 x3 y2 y3 y3 x x x y x y x2 y x2 y xy xy y2 y2

h r

h

Distance and Midpoint Formulas Binomial Theorem
x x x x y y y y
2 3 3

Distance between P1 x1, y1 and P2 x 2, y2 : y2 3xy 2 3xy 2 nn 2 n n k k x y k y3 y3 1 x n 2y2 nxy n 1 k 1

x2 x3 x3 xn

2xy 3x 2 y 3x 2 y nx n 1y

x

y

2

x2

2xy

y2 d s x2 x1
2

y2

y1

2

n

Midpoint of P1 P2 :

x1 2

x 2 y1 ,

y2 2

yn

Lines
Slope of line through P1 x1, y1 and P2 x 2, y2 : m y2 x2 y1 x1

n where k

nn

1 n 1 2 3

k

Quadratic Formula
If ax 2 bx c 0, then x b sb 2 2a 4ac .

Point-slope equation of line through P1 x1, y1 with slope m: y y1 mx x1

Inequalities and Absolute Value
If a If a If a If a If a b and b b, then a b and c b and c 0, then x x x a means a means a means x x a a or x a or a x a x a c, then a c b c. c. cb. cb.

Slope-intercept equation of line with slope m and y-intercept b: y mx b

0, then ca 0, then ca

Circles
Equation of the circle with center h, k and radius r: x h
2

y

k

2

r2

R E F E R E N C E PA G E 2

TRIGONOMETRY
Angle Measurement
radians 1 s r in radians cot 1
hyp ¨ adj

Fundamental Identities
r ¨ r s

180 rad 1 rad 180

csc tan

1 sin sin cos 1 tan tan 2 sec 2 sin tan

sec cot sin 2 1 cos sin

1 cos cos sin cos 2 cot 2 1 csc 2 cos cos

180

Right Angle Trigonometry
sin cos tan opp hyp adj hyp opp adj csc sec cot hyp opp hyp adj adj opp

sin
opp

tan

2

cos

2

sin

tan

2
B

cot

Trigonometric Functions
sin cos tan y r x r y x csc sec cot r y r x x y
¨ x y (x, y) r c

The Law of Sines
sin A a sin B b sin C c

a C

The Law of Cosines
a2 b2 b2 a2 a2 c2 c2 b2 2bc cos A 2ac cos B 2ab cos C
A b

Graphs of Trigonometric Functions
y y=sin x 1 π 2π x _1 _1 π 2π x π 1 2π x y y=cos x y y=tan x

c2

Addition and Subtraction Formulas
sin x sin x cos x y y y y y y sin x cos y sin x cos y cos x cos y cos x cos y cos x sin y cos x sin y sin x sin y sin x sin y

y 1

y=csc x

y 1

y=sec x

y

y=cot x

cos x tan x

tan x tan y 1 tan x tan y tan x tan y 1 tan x tan y

π _1

2π x _1

π

2π x

π

2π x

tan x

Double-Angle Formulas
sin 2x 2 sin x cos x cos 2x 1 sin 2x 2 cos 2x 1 1 2 sin 2x

Trigonometric Functions of Important Angles radians 0 30 45 60 90 0 6 4 3 2 sin 0 12 s2 2 s3 2 1 cos 1 s3 2 s2 2 12 0 tan 0 s3 3 1 s3 —

cos 2x tan 2x

2 tan x tan2x

Half-Angle Formulas
sin 2x 1 cos 2x 2 cos 2x 1 cos 2x 2

SINGLE VARIABLE

CA L C U L U S
EARLY TRANSCENDENTALS
SEVENTH EDITION

JAMES STEWART
McMASTER UNIVERSITY AND UNIVERSITY OF TORONTO

Australia . Brazil . Japan . Korea . Mexico . Singapore . Spain . United Kingdom . United States

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