Download TRIGONOMETRY Basic Graphs Identities

Cost
+ tan
t
2
i
— sins sin!
—
sinr
tan(s — I)
cos(s — t)
sin(s — t)
-
t — I
2
2cos
\
1 + cost
/----———
2
—
t)
s—I
-
s+t
-
I
r)
2t
tan—
2
tan
2 tsar
I — Cost
sort
1 —tant
-
sirs
sint
± cos (s — t)
=
—
.
s+r
S—t
2Cos—--—coc—-—-
=
sina
-
? -2bc
os a
Sifl
stny
s+t
S—f
coas —Cost =—2sin----——sin-------
Coss +cost =
Laws of Sines and Cosines
V
coss
— tan
1 -I- tan a tan
= Cos(s +
Factoring Formulas
2cos——-sIn-—,-—
—
cott
2sinssint =Cos(s—t) —cos(5 +r)
2 cos a cost
Product Formulas
2
1
cos±
—
cost + sins
tan .c
cos
1
+ COtf = CSCf
+ cos
2t
taft
I
tan —i) = —tan
1
5jn?
cott
sins cost
Half Angle Formulas
= sin(s + n + sin(s
sins — sint
sins
—
Double Angle Formulas
tan s tan t
— sin
, = 1 — 2sin’t
t
2
sinr
Addition Formulas
——-——
.1 — COSt
---——-
—
cos (—t) = Cost
2coccsinr=sin(s + t) —sin(s— r)
2 sinscost
2
\
= cos
t
2
cos(
Odd-even Identities
tans + tan t
-
2 srnr cost
Sin—±
t
cos2t
sin 2r
tan(s -It)
Sin,
srnt
Cofunction Identities
CSC t =
COtt
Cost
Basic Identities
sinscost + coss sins
—sin
cos(s + r = cos a cost
sin(s + t)
sin (—t)
cost
scct
sin(- —t) =
I
—
cost
=--—
Sect =
taft
Sin,
-
=
=
Vt
x
=
-
3-V;
V=SeCT
tanG
0
.fifl
tant
sin t = Sin
1’
t
=
x
v
—
x
—
r
a
—
a
b
=
iy=CSCII
=
=
b)
-
L
1
J
0
Cos 0
Cot I = Cot
cost
Graphs
0)
TRIGONOMETRY
U-
5)
-
V =
v
(1
=
x
v.0
cos°(1,x)
= SeC
tan y—/2
7
-
x +
+
+
+
+
—
+..
-I-
(p’
k)
+x)
±
2
p(p—l
)
)(p—
k!
i
.t
x
sinh x
<1
± e)
coshx
srnh x
1 (e’
ac/2
/2
+, —1<
—1x1
—I <x<1
csch x
cosh
=
sr,y
< y <
(p —k +1)
+
2
x
C’
6
.t
coshxl ±—±-±--
=
cos x =1 —
—
el+x++j+
5
X+X-+X-±
Series
tan°xx—--+——-—±.
sinh x
y
Hyperbolic Functions
— e’)
cosh x
—--1
I —x
sech x
5+
x
secix
sec’ x
tan tx
sinhx
tanhx=—
cosh x
sinh x
siny,—n-/2
yCOSx+?X=CoSv,0yar
= sin°x +s x =
Inverse Trigonometric Functions
y
area
rr + crr’v r + h
4
I liter
t000 cubic centimeters
=
7.48 gallons
453.6 grams
1 pound
1 cubic foot
2.20 pounds
180 degrees
=
0.62 miles
1 .057 quarts
1 kilometer
1’ =-rr
-
2
= irr
h
2
=
2
S = 42cr
CONVERSIONS
Volume
Surface
Spheres
Volume
Surface area
S
V = 7rrh
Volume
Cones
2 + 2crrh
S = 2irr
Surface area
radians
=
I liter
A =
Area
CIinders
C = 27cr
Circumference
Cirdes
2.54 centimeter5
cç
+ b =
1 kiloeram
=
1 inch
O
Any triangle
Right triangle
a2
Pythagorean Theorem
Triangles
GEOMETRY
0
U-
(U
/
19.
18.
17.
16.
15.
14.
13.
12.
ii.
10.
9.
8.
7.
6.
secu + C
u do
—
cot UI + C
= In Isec u + tan UI + C
csc u do = In ese o
sec
cotu du = Inlsinol + C
tanu do = —Inicosul + C
csc u cot u do = sc o + C
seco tano do
csc
u
2
du = —cotu ± C
o do = tanu + C
2
sec
do
2
=
a
J
zi\/
—
1
a
a
In
a
[—r==du =-sec’
/
+u2
J •\/5_.
a
+ C
+ C
C
1 —--rdu=sin±
a
1 2---—du tan1+C
J a
f
f
J
f
f
J
—cosu + C
ma
cosudo = sinu + C
sinudu
a”du
j
5.
c’ + C
j c’ do
4.
+C,n —1
do
—u’
—
fidt=lnIu!+c
fundu
oc
3
2.
1. fu etc =
INTEGRALS
U-
V.
0:
cv
D, tan
x =
Dsin’x
DYer =
Dr in x
D, tanh x
1
1 +
-
2x
sech
Dvsec’x
x’Vx —1
=—
D, cos’ x =
1
x In a
Dra’ = a’lna
D, log., x
D, cschx = —cschxcothx
D,sechx = —sechxanhx
D,cothx = —csch
x
2
Dr sinh x = cosh x
sinh x
D,cscx = —cscxcotx
Drsecx = secxtanx
D, cosh x
2x
Dr cot x = —csc
D cos x = —sin x
x
x
2
Drtanx = sec
Drsinx = cosx
D,x’ = r’
1
DERIVATIVES
Varberg, Purcell, and Rigdon
CALCULUS, 9/E
to accompany
Formula Card