Download Special Constants Special Products Special Factorizations Formulas

cob19421_es.indd
Sec1:2
12/22/08
9:52:54
PM user-s178
cob19421_es.indd
PagePage
Sec1:2
12/22/08
9:52:54
PM user-s178
/Users/user-s178/Desktop/22:12:08
/Users/user-s178/Desktop/22:12:08
Special
Constants
Special
Constants
� �
� 3.1416
� ��3.1416
� 2.7183
e � e2.7183
Formulas
from
Analytical
Geometry:
1 S
2 S
Formulas
from
Analytical
Geometry:
P1 PS
(x1(x
, y11,),y1P),2 PS
(x2(x
, y22,)y2)
� �
� � � 3.1416
� 3.1416
2 2
� � � 1.0472
� 1.0472
3 3
� 1.4142
12 12
� 1.4142
� 1.7321
13 13
� 1.7321
� � � 0.5236
� 0.5236
6 6
13 13 � 0.8660
� 0.8660
2 2
� � � 0.7854
� 0.7854
4 4
12 12 � 0.7071
� 0.7071
2 2
� � � 0.2618
� 0.2618
12 12
13 13 � 0.5774
� 0.5774
3 3
Distance
between
1 and
Distance
between
P1 P
and
P2 P2
Special
Products
Special
Products
2
2
� b21a
1a �1ab21a
� b2��b2a2��a b2� b
2
2
2
2 b2 2
� 2ab
1a �1ab2�
� a ��a 2ab
� b2� b
3
3
2
2
3
3 b2 3
� 23ab
1a �1ab2�
� a ��a 3a�2b3a� b3ab
� b3� b
2
��
b2xab��ab1x��1xa21x
� a21x
x2 �x 1a��1ab2x
� b2� b2
2
2
2
2 b2
� 2ab
a2 �a 2ab
� b2��b 1a��1ab2�
2
2
� b21a
a2 �a b2��b 1a��1ab21a
� b2� b2
2
2
2
2 b2
� 2ab
a2 �a 2ab
� b2��b 1a��1ab2�
Special
Factorizations
Special
Factorizations
� �
3
3
2
2
3
2 1a � ab 2
a3 �a b3��b 1a��1ab2�1ab2
� ab � b �2 b 2
3
2
Rectangle
Rectangle
2
� b21a
a3 �a b3��b 1a��1ab21a
� ab��abb2�2 b 2
Parallelogram
Parallelogram
A �Abh� bh
w
w
� 2w
P �P2l��2l2w
A �Alw� lw
h
Triangle
Triangle
Trapezoid
Trapezoid
h
Right
Triangle
Right
Triangle
B
B
of angles
SumSum
of angles
A A
A
�
B
�
C
�
180°
A � B � C � 180°
C
Ellipse
Ellipse
� �ab
A �A�ab
2
2
2
� 221a
C �C��
221a
� b2�2 b 2
a
c
Pythagorean Theorem
C Pythagorean Theorem
2
2
2
a2 �a b2��b c2� c
b
1 1 bh
bh
A �A �
2 2
c
a
a
a
4 4 ab
ab
A �A �
3 3
a
b
b
b
b
r
3
� lwh
V �Vlwh
� wh
S � Slw��lwlh��lhwh
V �Vs3� s
2
S � S6s�2 6s
Right
Circular
Cone
Right
Circular
Cone
Right
Square
Pyramid
Right
Square
Pyramid
1 12 �r2h
V �V �
�r h
3 3
�1r�r
S � S�r
�1rs2� s2
CoburnAlg&Trig2e10lbj_SE_ES.indd 1
ISBN: 0073519529 & 0073519421
Front
Author:
Coburn
0-4-4-4
ISBN:
0-07-351942-1
Front
endsheets
ISBN:
0-07-351942-1
Front
endsheets
Title:
Algebra
&
Trig
and
Precalculus,
Author:
John
W.
Coburn
Color:
Author: John W. Coburn
Color: 5 5
2e
Title:
College
Precalculus,
2e
Pages:
Title: College Precalculus, 2e
Pages:
2, 32, 3
1 2 1 b2h
V �V �
bh
3 3
2
2
2
2
� b2b
S � Sb2��b b2b
� 4h�2 4h
Dependent
(Coincident)
Lines
Dependent
(Coincident)
Lines
Slopes
Unequal:
m1m� m2
Slopes
Are Are
Unequal:
m1 �
2
Slopes
y-Intercepts
Equal:
m1m�, m
2, b1 � b2
Slopes
and and
y-Intercepts
Are Are
Equal:
m1 �
2 b1 � b2
y
y b � x
� log
bx 3
y � ylog
bx 3 b � x
logblog
b �b b1 � 1
x
bbx� x
logblog
bx �
blogbbx � x � x
M M � log M � log N
b
b
logblogb�Nlog
b M � logb N
N
nt r
a1r �
b nb
A �AP�
a1P�
n
1
logblog
1 �b 10 � 0
x bx
logblog
logc log
x �c x � log c
log c b
logb x
b
#
M P�# log
P log
bM
logblog
MPb�
bM
P
S initial
deposit,
S periodic
payment
P SPinitial
deposit,
p Spperiodic
payment
r r
S interest
per time
period
R SRinterest
rate rate
per time
period
a ba n b
n
nt
Accumulated
Value
of an
Annuity
Accumulated
Value
of an
Annuity
p p �11 �nt R2 nt � 1�
A �A ��11R�
R2 � 1�
R
Sequences
Series:
Sequences
andand
Series:
� �
S compounding
periods/year
n Sncompounding
periods/year
S time
in years
t S ttime
in years
Interest
Compounded
Continuously
Interest
Compounded
Continuously
�rt Pert
A �APe
Payments
Required
to Accumulate
Amount
Payments
Required
to Accumulate
Amount
A A
AR AR
p � p � 11 �nt R2 nt � 1
11 � R2 � 1
Sterm,
1st term,
S term,
nth term,
S sum
n terms,
S common
difference,
S common
a1 Sa11st
an Sannth
Sn SSnsum
of n of
terms,
d Sdcommon
difference,
r Srcommon
ratioratio
b
Formulas
from
Solid
Geometry:
SS
surface
area,
VS
volume
Formulas
from
Solid
Geometry:
SS
surface
area,
VS
volume
Cube
Cube
Intersecting
Lines
Intersecting
Lines
1
Interest
Compounded
n Times
Interest
Compounded
n Times
perper
YearYear
r
� �
Rectangular
Solid
Rectangular
Solid
Slopes
a Product
of �1:
1m2 � �1
Slopes
HaveHave
a Product
of �1:
m1mm
2 � �1
S interest
per year
r Srinterest
rate rate
per year
b
a
a
Slopes
Equal:
m1m� m2
Slopes
Are Are
Equal:
m1 �
2
S amount
accumulated
A SAamount
accumulated
h
h
Right
Parabolic
Segment
Right
Parabolic
Segment
a
Perpendicular
Lines
Perpendicular
Lines
� log
b M � logb N
logblog
MNb MN
� log
b M � logb N
�2 �r2
A �A�r
� 2�r
� �d
C �C2�r
� �d
b
Parallel
Lines
Parallel
Lines
1
Applications
Exponentials
Logarithms
Applications
of of
Exponentials
andand
Logarithms
Circle
Circle
a
Slope-Intercept
(slope
m, y-intercept
Slope-Intercept
FormForm
(slope
m, y-intercept
b) b)
��
mxb,�where
b, where
� mx1
y � ymx
b � by ��y1mx
� �
Triangle
Triangle
a
Point-Slope
Point-Slope
FormForm
� m1x
y � yy ��y1m1x
� x �2 x1 2
� �
s
P �Pns� ns
a aP
A �A �
P
2 2
h h
h h 1a � b2
A �A �
1a 2� b2
b b
2
b
b
Regular
Polygons
Regular
Polygon
s
s
P �P4s� 4s
2
A �As2� s
l
l
Square
Square
Equation
of Line
Containing
1 and
Equation
of Line
Containing
P1 P
and
P2 P2
Logarithms
Logarithmic
Properties
Logarithms
andand
Logarithmic
Properties
2
Formulas
from
Plane
Geometry:
PS
perimeter,
CS
circumference,
AS
area
Formulas
from
Plane
Geometry:
PS
perimeter,
CS
circumference,
AS
area
� �
Equation
of Line
Containing
1 and
Equation
of Line
Containing
P1 P
and
P2 P2
1
3
3
2
2
3
3 b2 3
� 23ab
1a �1ab2�
� a ��a 3a�2b3a� b3ab
� b3� b
¢y ¢yy2��y2y1� y1
m �m � �
¢x ¢xx2 �x2x1� x1
2
2
� 21x
2 �2 x1 2 � 1y2 �2 y1 2
d � d21x
2 � x1 2 � 1y2 � y1 2
� �
2
��
b2xab� ab
1x �1xa2�1x a2
�1xb2��b2x2��x 1a��1ab2x
2
2
2
2 b2 2
� 2ab
1a �1ab2�
� a ��a 2ab
� b2� b
Slope
of Line
Containing
1 and
Slope
of Line
Containing
P1 P
and
P2 P2
Right
Circular
Cylinder
Right
Circular
Cylinder
�2h�r2h
V �V�r
� 1r
2�r
S � S2�r
�1rh2� h2
Sphere
Sphere
4 34 �r3
V �V �
�r
3 3
� 24�r2
S � S4�r
Arithmetic
Sequences
Arithmetic
Sequences
Geometric
Sequences
Geometric
Sequences
� .2d,
� 12d
a1, aa21,�a2a1��a1d,�a3d,�a3a1��a12d,
. . ,. a. n. ,�ana1��a11n��1n12d
n
n
1a1a �2 an 2
Sn �Sn �
1a1 �
n
2 2
n
n
� 12d�
�2a1 �2a
� 11n��1n12d�
Sn �Sn �
2 2
2
a1rn�1
a1, aa21,�a2a1�r, aa13r,�a3a1�r2,a.1r. ., ,. a. n. ,�ana1�rn�1
n
a1 �a1a1�rna1r
Sn �Sn � 1 � r
1�r
a1 a1 ; �r� 6 1
S
�
Sq �q 1 ;��r�r 6 1
1�r
Binomial
Theorem
Binomial
Theorem
� �
n n 0 n n n�1 1 n n n�2 2
n
n 0 n
n n
1 n�1 n
# # a � na ba
n b2 �
1 ba
n b
b ab1 �b a �b aan�2
b ab2 �b # �# # # �
a0bba
1a �1ab2�
� a b aan0bb0a�b a�b aan�1
bn�1b � a �ba
1
2
n
�
1
0
1
2
n�1
n n
# # 132122112 a n b a�n b � n! n! ; ; 0! �0!1� 1
��
n1n121n
� 121n
# # #132122112
n! �n!n1n
� 22�# 22
� k2!
k k k!1n k!1n
� k2!
1/8/09 2:41:04 PM
cob19421_es.indd Page Sec1:3 12/22/08 9:52:56 PM user-s178
�
/Users/user-s178/Desktop/22:12:08
The Toolbox and Other Functions
linear
�
linear
y
y
identity
constant
y
y � mx � b
y
Fundamental Counting Principle: Given an experiment with two tasks completed in sequence, if the first can be
completed in m ways and the second in n ways, the experiment can be completed in m � n ways.
y�b
y�x
Permutations—Order Is a Consideration: (Al, Bo, Ray) and (Ray, Bo, Al) finish the race in a different order.
n!
.
The permutations of r objects selected from a set of n (unique) objects is given by nPr �
(n � r)!
Combinations—Order Is Not a Consideration: (Al, Bo, Ray) and (Ray, Bo, Al) form the same committee.
n!
.
The combinations of r objects selected from a set of n (unique) objects is given by nCr �
r!(n � r)!
Basic Probability: Given S is a sample space of equally likely events and E is an event defined relative to S.
n(E)
, where n1E2 and n1S2 represent the number of elements in each.
The probability of E is P(E) �
n(S)
For any event E1: 0 � P1E1 2 � 1 and P1E1 2 � P1~E1 2 � 1.
(0, b)
(0, b)
x
x
x
y � mx � b
squaring
y
m � 0, b � 0
cubing
y
square root
y
y
y � x2
y � �x�
x
y � x3
y � �x
x
cube root
x
floor function
reciprocal quadratic
y
�
1
x
P1E1 � E2 2 � P1E1 2P1E2 2
P1E1 ´ E2 2 � P1E1 2 � P1E2 2 � P1E1 � E2 2
y
y
circle with center
at (h, k)
1
y � x2
3
y � �x
r
x
1 2
x
x
x
k
exponential
exponential
y
logarithmic
y
bx
x2
y�c
y � b�x
y � logb x
y�
x
h
�
y2
�
(�a, 0)
�
(c, 0)
1
x
(0, 1 �c a )
vertical reflections
vertical stretches/compressions
S
y � af 1x � h2 � k
S
y � f 1x2
S
Transformation of Given Function
horizontal shift h units,
opposite direction of sign
vertical shift k units,
same direction as sign
hyperbola with center
at (h, k)
k
(h, k)
central
hyperbola
(x � h)2
a2
�
(y � k)2
b2
(0, b)
�
y2
b2
�1
�1
x
If a � b, the ellipse
is oriented vertically.
x2
a2
�
y2
b2
p�0
( p, 0)
x
(0, p)
�1
x
x
If term containing y leads, the
hyperbola is oriented vertically.
(0, �b)
y
x2 � 4py
vertical parabola
focus (0, p)
directrix y � �p
y
y � �p
(c, 0)
h
For linear function models, the average rate of change on the interval 3 x1, x2 4 is constant, and given by the slope formula:
¢y
y2 � y1
�
. The average rate of change for other function models is non-constant. By writing the slope formula in function form
x2 � x1
¢x
using y1 � f 1x1 2 and y2 � f 1x2 2, we can compute the average rate of change of other functions on this interval:
(y � k)2
b2
c2 � |a2 � b2|
(�c, 0)
Average Rate of Change of f(x)
�
(a, 0)
x2
a2
x
Transformations of Basic Graphs
Given Function
(h � a, k)
(x � h)2
a2
h
c
1 � ae�bx
y
�
(�c, 0)
(0, � b)
x
x
ellipse with center
at (h, k), a � b
(0, b)
r2
1
1
(h, k)
(h, k � b)
central
ellipse
(x, y)
(0, 0)
y
y
(h � a, k)
(x � h)2 � (y � k)2 � r2
r
logistic
k
(h, k � b)
(h, k)
central
circle
y�
Probability of E1 or E2
Conic Sections
y
y�
Probability of E1 and E2
x
reciprocal
y
y � �x�
y
x
m � 1, b � 0
m � 0, b � 0
m � 0, b � 0
absolute value
Quick Counting and Probability
p�0
x � �p
y2 � 4px
horizontal parabola
focus ( p, 0)
directrix x � �p
�1
c2 � a2 � b2
f(x2) � f(x1)
�y
�
�x
x2 � x1
CoburnAlg&Trig2e10lbj_SE_ES.indd 2
ISBN: 0073519529 & 0073519421
Author: Coburn
ISBN: 0-07-351942-1
Title: Algebra & Trig and Precalculus,
Author: John W. Coburn
2e
Title: College Precalculus, 2e
1/8/09 2:41:04 PM
Front
0-4-4-4
Back endsheets
Color: 5
Pages: 4, 5
cob19421_es.indd Page Sec1:3 12/22/08 9:52:56 PM user-s178
�
/Users/user-s178/Desktop/22:12:08
The Toolbox and Other Functions
linear
�
linear
y
y
identity
constant
y
y � mx � b
y
Fundamental Counting Principle: Given an experiment with two tasks completed in sequence, if the first can be
completed in m ways and the second in n ways, the experiment can be completed in m � n ways.
y�b
y�x
Permutations—Order Is a Consideration: (Al, Bo, Ray) and (Ray, Bo, Al) finish the race in a different order.
n!
.
The permutations of r objects selected from a set of n (unique) objects is given by nPr �
(n � r)!
Combinations—Order Is Not a Consideration: (Al, Bo, Ray) and (Ray, Bo, Al) form the same committee.
n!
.
The combinations of r objects selected from a set of n (unique) objects is given by nCr �
r!(n � r)!
Basic Probability: Given S is a sample space of equally likely events and E is an event defined relative to S.
n(E)
, where n1E2 and n1S2 represent the number of elements in each.
The probability of E is P(E) �
n(S)
For any event E1: 0 � P1E1 2 � 1 and P1E1 2 � P1~E1 2 � 1.
(0, b)
(0, b)
x
x
x
y � mx � b
absolute value
squaring
y
m � 0, b � 0
cubing
y
square root
y
y�
y � �x�
y
x2
x
y�
x3
y � �x
x
cube root
x
floor function
reciprocal quadratic
y
�
Probability of E1 or E2
P1E1 � E2 2 � P1E1 2P1E2 2
P1E1 ´ E2 2 � P1E1 2 � P1E2 2 � P1E1 � E2 2
Conic Sections
y
y
y�
Probability of E1 and E2
x
reciprocal
y
y � �x�
y
x
m � 1, b � 0
m � 0, b � 0
m � 0, b � 0
Quick Counting and Probability
1
x
y�
3
y
circle with center
at (h, k)
1
x2
y � �x
r
x
1 2
x
x
x
k
exponential
y
logarithmic
y
y � bx
y � logb x
y�
x
h
(�a, 0)
1
x
(0, 1 �c a )
�
x2
a2
x
vertical reflections
vertical stretches/compressions
S
y � af 1x � h2 � k
S
y � f 1x2
S
Transformation of Given Function
horizontal shift h units,
opposite direction of sign
vertical shift k units,
same direction as sign
hyperbola with center
at (h, k)
k
(h, k)
central
hyperbola
(x � h)2
a2
�
y2
b2
�1
�1
x
If a � b, the ellipse
is oriented vertically.
(y � k)2
b2
(c, 0)
x2
a2
�
c2 �
y2
b2
p�0
( p, 0)
x
(0, p)
�1
x
x
If term containing y leads, the
hyperbola is oriented vertically.
(0, �b)
y
x2 � 4py
vertical parabola
focus (0, p)
directrix y � �p
y
y � �p
h
For linear function models, the average rate of change on the interval 3x1, x2 4 is constant, and given by the slope formula:
¢y
y2 � y1
�
. The average rate of change for other function models is non-constant. By writing the slope formula in function form
x
¢x
2 � x1
using y1 � f 1x1 2 and y2 � f 1x2 2, we can compute the average rate of change of other functions on this interval:
�
(0, b)
(�c, 0)
Average Rate of Change of f(x)
(y � k)2
b2
c2 � |a2 � b2|
Transformations of Basic Graphs
Given Function
�
(a, 0)
h
y
�
(c, 0)
(0, � b)
x
x
(�c, 0)
c
1 � ae�bx
1
1
(h � a, k)
(0, b)
x2 � y2 � r2
y�c
y � b�x
(x, y)
ellipse with center
at (h, k), a � b
(x � h)2
a2
(h, k � b)
central
ellipse
(0, 0)
y
y
(h, k)
(x � h)2 � (y � k)2 � r2
r
logistic
(h � a, k)
(h, k)
central
circle
exponential
k
(h, k � b)
p�0
x � �p
y2 � 4px
horizontal parabola
focus ( p, 0)
directrix x � �p
�1
a2 � b2
f(x2) � f(x1)
�y
�
�x
x2 � x1
CoburnAlg&Trig2e10lbj_SE_ES.indd 3
ISBN: 0073519529 & 0073519421
Author: Coburn
ISBN:
0-07-351942-1
Title:
Algebra
& Trig and Precalculus,
Author:
John W. Coburn
2e
Title: College Precalculus, 2e
1/8/09 2:41:05 PM
Back
4-4-4-0
Back endsheets
Color: 5
Pages: 4, 5
cob19421_es.indd
Sec1:4
12/22/08
9:52:57
PM user-s178
cob19421_es.indd
PagePage
Sec1:4
12/22/08
9:52:57
PM user-s178
/Users/user-s178/Desktop/22:12:08
/Users/user-s178/Desktop/22:12:08
Commonly
used,
small
case
Greek
letters
Commonly
used,
small
case
Greek
letters
Fundamental
Identities
Fundamental
Identities
� �
� �
alpha
alpha
betabeta
gamma
gamma
deltadelta
�
�
zeta zeta
thetatheta
lamda
lamda
mu mu
pi pi
rho rho
sigma
sigma
phi phi
psi psi
omega
omega
epsilon
epsilon
Trigonometric
Functions
a Real
Number
Trigonometric
Functions
of of
a Real
Number
� �
Reciprocal
Identities
Reciprocal
Identities
Ratio
Identities
Ratio
Identities
Pythagorean
Identities
Pythagorean
Identities
1 1
sec sec
� �
cos cos sin sin tan tan
� �
cos cos �2cos
�21 � 1
sin2sin�2cos
sin1�2
� �sin
sin1�2
� �sin
1 1
csc csc
� �
sin sin cos cos cot cot
� �
sin sin �2sec2
�2tan�2sec
1 � 1tan
cos1�2
� cos cos1�2
� cos
�2cot�2csc
�2csc2
1 � 1cot
tan1�2
� �tan
tan1�2
� �tan
t
t
(x, y)(x, y)
number
on unit
the unit
circle
associated
P1x,P1x,
y2 ony2 the
For For
any any
real real
number
t andt and
pointpoint
circle
associated
withwith
t: t:
y y
; x0 � 0
cos tcos
� tx � x
sint sint
� y� y
tan t tant
� �
;x�
x x
1 1
1 1
x x
; x0 � 0
; y0 � 0
; y0 � 0
sectsect
� �
csctcsc
�t�
;y�
;y�
;x�
cot tcot
�t�
x x
y y
y y
1 1
cot cot
� �
tan tan r � 1r � 1
Cofunction
Identities
Cofunction
Identities
1
1
Trigonometry
Coordinate
Plane
Trigonometry
andand
thethe
Coordinate
Plane
x x
cos cos
� �
r r
y y
sin sin
� �
r r
y y
, x0 � 0
tan tan
� �
,x�
x x
r r
, x0 � 0
sec sec
� �
,x�
x x
r r
, y0 � 0
csc csc
� �
,y�
y y
x x
, y0 � 0
,y�
cot cot
� �
y y
a xb��xbcscx
� cscx
sec asec �
2 2
r
r
y
y
5
5
(x, y)(x, y)
a point
on terminal
the terminal
an angle
in standard
position:
P1x,P1x,
y2 a y2point
in standard
For For
on the
side side
of anofangle
position:
a xb��xbcot
�xcot x
tan atan �
2 2
y
y
� �
r r
�5
�5
5
x
5
x
x
Sum
Difference
Identities
Sum
andand
Difference
Identities
� �
� xcos x
sin asina
� xb��xbcos
2 2
x
� �
�xsin x
� xb��xbsin
cosacosa
2 2
cos1
� cos
� sin
cos1
� 2��2cos
coscos� sin
sinsin �xtan x
a xb��xbtan
cot acot �
2 2
� tan tantan
� tan
tan1
tan1
� 2��2 �
� tan tan
1 �1 tantan
Double-Angle
Identities
Double-Angle
Identities
Half-Angle
Identities
Half-Angle
Identities
2
Right
Triangle
Trigonometry
Right
Triangle
Trigonometry
�5
2
� 2cos
� 2cos
�21 � 1
�5
2
� 2sin
2
� 1�
� 12sin
indicated
adjacent
opposite
to acute
angle
¢ABC
For For
rightright
¢ABC
withwith
indicated
sidessides
adjacent
and and
opposite
to acute
angle
: :
adj adj
coscos
� �
hyp hyp
opp opp
sinsin
� �
hyp hyp
opp opp
tan tan
� �
adj adj
hyp hyp
sec sec
� �
adj adj
hyp hyp
csccsc
� �
opp opp
adj adj
cotcot
� �
opp opp
hyp hyp
opp opp
� 122
cos 122
1 � 1cos
sin2sin�2 �
2 2
� cos 1 � 1cos
cos cos
� �� �
2 2 A A2 2
� 122
cos 122
1 � 1cos
�2 �
cos2cos
2 2
Product-to-Sum
Identities
Product-to-Sum
Identities
Special
Triangles
Special
Angles
Special
Triangles
andand
Special
Angles
B
0° 0°
0
0
1
1
0
0
1
13
1
30° 30°
1
2
1
2
13
2
13
2
1
13
45° 45°
12
2
12
2
12
2
12
2
1
60° 60°
13
2
13
2
1
2
1
2
90° 90°
1
1
0
0
— —
2
2
12 12
13 13
2
13
2
13
— —
1
1
1
1
— —
2
13
2
13
13 13
12 12
2
2
— —
B
B
1
1
1
13
1
13
0
0
60� 60�
45� 45�
√2x √2x
A 45�
A 45�
1x 1x
B
2x 2x
1x 1x
C C
A 30� 30�
A
√3x √3x
1
y �t csc t
y � csc
y
1
1
1
2
�1
�1
2
3
2
3
2
y
1
y
C C
1 1
�cos1
� cos1
� 2�
�cos1
� 2��2cos1
� 2�
cos cos
coscos
� �
2 2
2
t2 t
�1
�1
CoburnAlg&Trig2e10lbj_SE_ES.indd 4
ISBN: 0073519529 & 0073519421
Back
Author: Coburn
4-4-4-0
ISBN:
0-07-351942-1
Front
endsheets
ISBN:
0-07-351942-1
endsheets
Title:
Algebra
& Trig and Precalculus, Front
Author:
John
W.
Coburn
Color:
5
Author:
John
W.
Coburn
Color:
5
2e
Title:
College
Precalculus,
Pages:
Title:
College
Precalculus,
2e 2e
Pages:
6, 76, 7
2
�� �� �sin
2 cosa b sinbasin a b b
sin sin
�sin
�2 �
cosa
2 2
2 2
�� �� b cosa b b
� cos
2 cosa b cosa
cos cos
�cos
�2 �
cosa
2 2
2 2
� 4 , 1�� 4 ,
3
2
3
2
2
t2 t �
� �
2
2
�2
�1
�1
2
� �
1�
�� �� b sina b b
� cos
� sina
�2 sin a b sina
cos cos
�cos
��2
2 2
2 2
Sines
LawLaw
of of
Sines
y �t tan t
y � tan
1
y �tcos t
y � cos
2
�� �� bcosa b b
�sin
2 sina bcosa
sin sin
�sin
�2 �
sina
2 2
2 2
1 1
�cos1
� cos1
� 2�
sin sin
sinsin
� �
�cos1
� 2��2cos1
� 2�
2 2
y
y �t sec t
y � sec
y �t sin t
y � sin
1 1
�sin1
� sin1
� 2�
�sin1
� 2��2sin1
� 2�
sin sin
coscos
� �
2 2
1 1
�sin1
� sin1
� 2�
�sin1
� 2��2sin1
� 2�
cos cos
sinsin
� �
2 2
Graphs
Trigonometric
Functions
Graphs
of of
thethe
Trigonometric
Functions
y
� �
1x 1x
� �
y
Sum-to-Product
Identities
Sum-to-Product
Identities
� �
� sin �sin� cos �cos � tan�tan� csc �csc � sec �sec � cot �cot �
C C
sin Asin Asin Bsin Bsin Csin C
� � � �
a a b b c c
3
2
t 3 t
y �t cot t
y � cot
2
Area
a Triangle
Area
of of
a Triangle
� �
1 1
bcAsin A
A �A �
bc sin
2 2
� 122
cos 122
1 � 1cos
tan2tan�2 �
� 122
cos 122
1 � 1cos
sin sin � �
� cos
1 � 1cos
adj adj
� �
�
� cos 1 � 1cos
� �
tan tan
2 2 sin sin 2 tan2tan tan122
tan122
� �
�2 tan
1 � 1tan
2
� �
� cos 1 � 1cos
sin sin
� �� �
2 2 A A2 2
2
cos122
� cos
� sin cos122
� cos
�sin
� �
Power
Reduction
Identities
Power
Reduction
Identities
� �
sin122
� 2sin
sin122
� 2sin
coscos 2
�sin
� cos
sin1sin1
� 2��2sin
coscos
�cos
sinsin �xsec x
a xb��xbsec
csc acsc �
2 2
� �
2
Identities
to Symmetry
Identities
duedue
to Symmetry
b
A
� 2bc
cos A
a2 �a2b2��b2c2��c22bc
cos A
b
A
a
c
c
B
Cosines
LawLaw
of of
Cosines
� �
a
� 2ac
cos B
b2 �b2a2��a2c2��c22ac
cos B
� 2ab
cos C
c2 �c2a2��a2b2��b22ab
cos C
B
1/8/09 2:41:06 PM