Algumas Frmulas para a Disciplina de Fundamentos de Matemtica
Equao do 2 Grau:
02 =++ cbxax
vrtice: )4
,2
(aa
bV
D--=
frmula de
Bskara:a
acbbx
242 --
=
))(( 21 xxxxa -- , 21 ,xx so as razes da equao.
ab
xx -=+ 21
ac
xx =21.
Produtos Notveis:
222 2)( bababa ++=+ 222 2)( bababa +-=- ))((22 bababa -+=-
32233 33)( babbaaba +++=+ 32233 33)( babbaaba -+-=-
))(( 2233 babababa ++-=- ))(( 2233 babababa +-+=+
Expoentes e Radicais:
nmnm aaa +=. nmnm aa .)( =
nmn
m
aaa -=
nnn baab =)( nmm n aa .=
nn
aa
1=-
nmnm aa )(
n
nn
ba
ba
=
nnn baab .=
mnn mnm
aaa )(==
Logaritmos:
xaxy ya == log
yxxy aaa logloglog +=
yxyx
aaa logloglog -=
xrx ar
a loglog = 01log =a 1log =aa
xx 10loglog = xx elogln =
Algumas Propriedades dos Logaritmos
NMNM aaa loglog).(log +=
NMNM
aaa logloglog -=
MNM aN
a log.log =
MN
MM aNaN
a log.1
loglog1
==
bN
Na
ab log
loglog =
ba
ab log
1log = ou 1log.log =ba ab
Nmero Binomial:
)!(!!
knkn
kn
-=
nnn ).1.....(5.4.3.2.1! -=
Algumas Relaes Trigonomtricas:
1cossen 22 =+ xx xx
tgxcossen
=
xx
tgxgx
sencos1
cot ==
xx
sen1
seccos =
xx
cos1
sec =
xxtg 22 sec1 =+ xgx 22 cot1seccos +=
Funes Circulares Inversas
xy 1sen -= ou yx arcsen= xy 1cos-= ou yx arccos=
xtgy 1-= ou arctgyx = xy 1seccos -= ou yx secarccos=
xy 1sec -= ou yarcx sec= xgy 1cot -= ou gyarcx cot=
Subtrao de Arcos
abbaba cos.sencos.sen)sen( -=- bababa sen.sencos.cos)cos(
+=-
tgbtgatgbtga
batg.1
)(+
-=-
Soma de 2 Arcos
abbaba cos.sencos.sen)sen( +=+ bababa sen.sencos.cos)cos(
-=+
tgbtgatgbtga
batg.1
)(-
+=+
gbgagbga
bagcotcot
1cot.cot)(cot
+-
=+
Outras converses circulares
aaa cos.sen22sen = aaaa 222 sen21sencos2cos -=-=
atgtga
atg21
22
-=
aaa 3sen4sen33sen -= aaa cos3cos43cos 3 -=
0 30 45 60 90
sen 0 21
22
23
1
cos 1 23
22
21
0
tg 0 33
1 3
cotg 3 1 33
0
sec 1 3
32 2 2
cossec 2 2 3
32 1
