Formulario De Calculo

REFERENCE PAGES

Algebra

Geometry

Arithmetic Operations
ab

c

a

ab

c

a
b
a
b
c
d

ac

a
b

b

Geometric Formulas

c
b

c
d

ad

bc

Formulas for area A, circumference C, and volume V :

ad
bc

Triangle
A 1 bh
2
1
2 ab sin

bd
d
c

a
b

a

Exponents and Radicals
x mx n

xm

n

xm
xn

x mn

xy

n

x nyn

x1 nxm

r

h

x
y

n

n

r

Sphere
V 4 r3
3

xn
yn

xm n

n
n
sx sy

¨

b

n

s

r

1
xn

n

x

n
sx

n
sxy

Sector of Circle
A 1r2
2
sr
in radians

¨

n

xm

Circle
A
r2
C 2r

A

(sx ) m

n
sx m

n

Cone
V 1 r 2h
3

4 r2

A

r sr 2

r

h

h

Factoring Special Polynomials

r

2

x

yx

x3

y3

xy x2

xy

y2

x3

y3

x

y x2

xy

y2

x

2

y

y

Distance and Midpoint Formulas
Binomial Theorem

Distance between P1 x1, y1 and P2 x 2, y2 :

x

y

2

x2

2 xy

y2

x

y

3

x3

3x 2 y

3xy 2

y3

x

y

3

x3

3x 2 y

3xy 2

y3

x

y

n

xn

n x n 1y

x

nn

y

2

nn

2

1
n
123

2 xy

y2Midpoint of P1 P2 :

x n 2y2

n nkk
xy
k
n
where
k

x2

d

1

k

n xy n

1

yn

x1
2

s x2

x 2 y1
,

bx

y2

y1

y2

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

sb 2
2a

b

4ac

.

If a

b and b

If a

b, then a

If a

b and c

0, then ca

y

cb.

If a

b and c

0, then ca

y1
x1

0, then

b

c.

y1

mxx1

cb.

If a

y2
x2

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

Inequalities and Absolute Value
c

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

c.
y

mx

b

Circles

x

a

means

x

a

means

x

a

means

2

2

m

c, then a

2

k

0, then x

c

x1

Lines

1

Q uadratic Formula
If ax 2

xa
x

or

a
x
a

x

a

x

a

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

a
or

h2

r

n
sx
n
sy

x
y

Cylinder
V
r 2h

x

❙❙❙❙

1

❙❙❙❙

h

2

y

k

2

r2

REFERENCE PAGES

Trigonometry
Angle Measurement
radians
1

180

s

F undamental Identities

180

1
sin

sec

1
cos

tan

sin
cos

cot

cos
sincot

180

1 rad

rad

csc

s

r

1
tan

sin 2

cos 2

¨
r

r
in radians

Right Angle Trigonometry
sin
cos
tan

opp
hyp

csc

adj
hyp

sec

opp
adj

sec 2

1

sin

sin

cos

tan

tan

sin

1
hyp
opp

cot

hyp

hyp
adj

opp

¨

tan 2

cot 2

cos

sin

2

csc 2
cos
cos

2

adj

adj
opp

tan

cot

2Trigonometric Functions
sin

y
r

r
y

csc

cos

x
r

sec

y
x

cot

sin A
a

(x, y)

r
x

tan

x
y

a
C

¨

The Law of Cosines

x

b

a2

2bc cos A

a2

c2

2ac cos B

c2

y=tan x

c2

b2
y

b2

a2

b2

2ab cos C

A

y=cos x

1

1
π

sin C
c
c

y
y=sin x

sin B
b

r

Graphs of TrigonometricFunctions
y

B

The Law of Sines

y

2π

Addition and Subtraction Formulas

2π

sin x

y

sin x cos y

cos x sin y

_1

sin x

y

sin x cos y

cos x sin y

cos x

y

cos x cos y

sin x sin y

y

cos x

y

cos x cos y

sin x sin y

tan x

y

tan x tan y
1 tan x tan y

tan x

y

tan x tan y
1 tan x tan y

x
_1

y

y=csc x

1

π

2πx

y

y=sec x

x

π

y=cot x

1
π

1

2π x

_1

π

2π x

2π x

π

_1

Double-Angle Formulas
sin 2 x

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

2 sin x cos x

cos 2 x

Trigonometric Functions of Important Angles

cos 2x

tan 2 x

0
s3 3
1
s3
—

1

sin 2x

2 cos 2x

1

1...