Formulario de aljebra

REFERENCE PAGES

Algebra
Arithmetic Operations
ab a b c c a b ab c b ac a b a b c d c d a b ad bd d c ad bc bc

Geometry
Geometric Formulas
Formulas for area A, circumference C, and volume V: Triangle A 1 bh 2 1 2 ab sin
a ¨

Circle A r2 C 2 r

Sector of Circle A 1r2 2 s r in radians

Exponents and Radicals
x mx n xm xy x1 n
n sxy

h r b ¨

r

s

xm x mn

n

xm xn xn

xm 1 xn
n

n

r

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 n sx sy

x y

n sx n sy

h r

h

Factoring Special Polynomials
x
2

y

2

x x x

y x y x2 y x2

y xy xy y2 y2

x3 x3

y3 y3

Distance and Midpoint Formulas Binomial Theorem
x x x x yy 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 m 0, then x b sb 2 2a 4ac . y2 x2 y1 x1
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 :

nwhere k

nn

1 n 1 2 3

k

Quadratic Formula
If ax 2 bx c

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 a a means means means x x a a a x or 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 mxb

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

❙❙❙❙

1

❙❙❙❙

REFERENCE PAGES

Trigonometry
Angle Measurement
radians 1 s r in radians cot 1 hyp opp hyp adj adj opp
¨ adj hyp opp

Fundamental Identities
180
r ¨ r s

180 rad 1 rad

csc tan

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

sec cot sin 2 1cos 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

sin 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
b

2bc cosA 2ac cos B 2ab cos C
A

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
2π x

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

π _1

2π x _1

π

2π x

π

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

❙❙❙❙

2❙❙❙❙

REFERENCE PAGES

Differentiation Rules
General Formulas
1. 3. 5. 7.

d c dx d f x dx

0 tx f x f xt x f tx t x t x txf x
(Product Rule)

2. 4. 6. 8.

d cf x dx d f x dx d dx f x tx

cf x tx f x txf x tx nx n
1

t x f xt x
2

d f xtx dx d f tx dx

(Quotient Rule)

(Chain Rule)

d xn dx

(Power Rule)

Exponential and Logarithmic Functions
9. 11.

d ex dxd ln x dx

ex 1 x

10. 12.

d ax dx d log a x dx

a x ln a 1 x ln a

Trigonometric Functions
13. 16.

d sin x dx d csc x dx

cos x csc x cot x

14. 17.

d cos x dx d sec x dx

sin x sec x tan x

15. 18.

d tan x dx d cot x dx

sec 2x csc 2x

Inverse Trigonometric Functions
19. 22.

d sin 1x dx d csc 1x dx

1 s1 x2 1 1 x sx 2

20. 23.

d cos 1x dx d sec 1x...