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K-
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.*5*32$%* :& 2*)$)& )* 9% "%#9:; )*: 49&: =* 4;%;4* L9* :& 2*)$)& )* =9 "%#9:; =9C:*2*%5&3$; *= I @*4*= :& 2*)$)& )* =9 "%#9:; 4;2C:*2*%5&3$;6 ?*=C9*=5&0 60º
N-
O& 2*)$)& )*: "%#9:; =9C:*2*%5&3$; )* x *= $#9&: & "%#9:; x Q 7- :& 2*)$)& )* =9 "%#9:; 4;2C:*2*%5&3$;6
123º 6
P&:49:*0 &- :& 2*)$)& )*: ?*=C9*=5&0 &-
57 º Q
7-
33º
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180º
Q 4&:49:* :& 2*)$)& )* 4&)& "%#9:; ?*=C9*=5&0
!
rad
8
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7! 3
rad Q Q 7-
100 ! 9
rad Q Q 4-
!5"
3
rad Q Q )-
!5"
9
rad Q Q *-
17 " !
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4!
rad Q Q /-
rad
3
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!
2!
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!
/-
rad
3
4-
*-
rad
3
rad
4 7"
rad
2 7!
rad
6 5!
rad
6
?*=C9*=5&0 &-
60º Q
7- 120º Q 4- ! 225º Q )- ! 630º Q *-
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=
?*=C9*=5&0 &- B
75º Q
=
!
12
/- 150º
V49": *= :& 2*)$)& *% 3&)$&%*=
4 B Q
19 " =
210º Q
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rad Q Q 7- A
4! =
5
rad Q Q B
! =
rad
5
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(315º)
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7- tan(150º )
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sen
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#-
sen
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cot
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2 2
Q 7- !
3 3
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3
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(
)
cos 300º
+ sen
(330º )
+
tan
( !135º ) ?*=C9*=5&0 (
(J- X=C*4$/$4&%); :;= 3*=9:5&);= C&34$&:*=Q 4&:49:* *: @&:;3 %92E3$4; )*0
! $ !5 $ ! $ & + sen # & ' tan # & "6% " 6 % "3%
3cos #
3 +1
?*=C9*=5&0
2
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cos
sen
3
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sen
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&- R
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sen
2
sen
7- (
4- +
" ! % + $# 3 ' & -,
)- H
3
*= $#9&: &0
*- I ?*=C9*=5&0 4-
(N- X=C*4$/$4&%); :;= 3*=9:5&);= C&34$&:*=Q 4&:49:* *: @&:;3 %92E3$4; )*0
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o
o
2
o
! $ # & cos ( ) "6% !3 $ !3 $ 4tan # sen & # & " 4 % " 4 % sen
b
=
2
2
2
?*=C9*=5&0
1 16
3
8
4
7
4 !"#$%& H )* +,
+R- X=C*4$/$4&%); :;= 3*=9:5&);= C&34$&:*=Q 4&:49:* *: @&:;3 %92E3$4; )*0
! $ ! $ 4tan ' & # & "3% "4% A ! $ 5 ' sen # & 3 "6%
3cos #
log c
(d ) Q =$
c
=
(60 ) cos (330 ) tan ( 45 ) ! (30 ) o
sen
d
=
o
+
o
o
sen
()
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1
+
2
)*/$%$); C;3 *:
!
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=
( )
1Q
cos !
=
tan ( ! ) no está definida Q
0 Q
( ) ( )
cot !
sec ( ! ) no está definida Q
0Q
=
csc !
=
1
7- P ( 6 ,!7 ) ?*=C9*=5&0 sen( ! )
7 85
( )
Q
"
=
85
cos !
6 85 =
85
tan !
=
"
6
85
( )
Q
7
( )
Q
sec !
=
6
Q
( )
cot !
( )
Q
csc !
6 =
"
7 85
=
"
7
4- P ( !3 ,!2 ) 2 13
?*=C9*=5&0 sen( ! )
=
"
13
Q
( )
cos !
3 13 "
=
13
( )
sec !
Q
( )
tan !
13 =
"
3
2 =
Q
3
Q
( )
cot !
( )
csc !
3 =
2
Q
13 =
"
2
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=
"
1 2
Q 4;%
?*=C9*=5&0
!
*% *: 5*34*3 49&)3&%5*6
( )
cos !
3 =
"
2
Q
( )
tan !
3 =
3
Q
( )
cot !
3 Q sec
=
( ) !
2 3 =
csc
7-
( )
cos !
3 =
4
Q 4;%
!
"
( ) !
3
Q
"2
=
*% *: 49&35; 49&)3&%5*6
?*=C9*=5&0 sen( ! )
7 =
"
4
Q
( )
tan !
7 =
"
3
Q
( )
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3 7 =
"
7
Q sec (! )
( )
csc !
4 =
3
Q
4 7 =
"
7 !"#$%& I )* +,
4-
tan
( ) !
=
3 , 4;%
*% *: C3$2*3 49&)3&%5*6
!
?*=C9*=5&0 sen( ! )
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10
Q
( )
cos !
10 =
10
Q
( )
cot !
1 =
3
Q sec ( ! )
( )
csc !
()
+H- 1*& :& /9%4$U% )* @&3$&7:* 3*&: f x &- R
7- (
"
=
10 Q
=
10 =
3
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1 ! 2sgn $ sen $
#
4- +
)- Y(
*- I ?*=C9*=5&0 )-
& ( ' ( + ( ' ( + ( ' ( + !# $ ! % 2 3 4 6 8 12 "
+I- P&:49:* *: @&:;3 &C3;>$2&); )*0 &- R
cos
7- (Z+
4- +
)- H
*- I ?*=C9*=5&0 7-
! $ # + + + & " 3 6 12 24 %
sen
e
+,- P&:49:* *: @&:;3 &C3;>$2&); )*0
(
cos 1140
o
) 3
?*=C9*=5&0
!
!3
log #100 + tan #
+J- P&:49:* *: @&:;3 &C3;>$2&); )*0
" 4
"
+
9 16
+
27 64
+
2e
2
$$ && %% ?*=C9*=5&0 +
+K- 1$ =* 4;%;4* L9*0
M
.*5*32$%* *: @&:;3 )*0
=
(
) ! 2 (!4620 )
csc 1560°
15 M
2
sen
°
A
N
=
! # ln e # "
! # "
!
! ! $$$ &&&& " 6 %%&%
cos# 2 ! # # sen#
"
$ & & %
! N ?*=C9*=5&0
6
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( )
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# " & !3 sen % " x ! ( ,x ) *+ !2 ,2 -, 2 ' $
=
HR- P;%=$)*3&%); :& /9%4$U% )*: *D*34$4$; &%5*3$;3Q &B;3& 7;=L9*D* :&= #3"/$4&= )*0
(
g ( x ) sgn f ( x ) =
)
A
(
h ( x ) = µ f ( x )
) !"#$%& , )* +,
H(- 1$ f :
"#!2,2 %$ *=5" )*/$%$)& C;3 f ( x )
=
2 sen
x
2
!
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( )
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(
)
*- f *= *=53$45&2*%5* 43*4$*%5* *% *: $%5*3@&:; !2, !1 6 ?*=C9*=5&0 7H+- O& #3"/$4& 2;=53&)& & 4;%5$%9&4$U% *= )* :& /9%4$U% 49A& 3*#:& )* 4;33*=C;%)*%4$& *=0
f ( x ) = Asen( Bx ) + D
.*5*32$%* :;= @&:;3*= )* :&= 4;%=5&%5*=0 A Q B A D 6
()
?*=C9*=5&0 f x
HH- [;=L9*D* :& #3"/$4& )* :& /9%4$U%
()
g x
! = sen
2
x
+
1,
=
3 sen
( x ) ! 2 !
x ! # $"4,4%&
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()
D t
5 =
2
& 1 t ' ( # $ ! % 2 6 "
sen
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?*=C9*=5&0
T
=
4 ! Q A
5 =
2
Q
" !
=
3
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()
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=
2
cos
(
x +
)
+
1;
x ! #$"3,5&% Q *=
G]O1a L9*0
()
&- f x
!
0 *%
5;); =9 );2$%$;6
7- X= 9%& /9%4$U% &4;5&)&6
( )
4- X= 43*4$*%5* *% *: $%5*3@&:; 2,3 6
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( ) 3 cos ( 2 x ) ,!2 " # x # 2 " 2 sen ( 4 x ) ,! " # x # "
&-
y
=
7-
y
=
4-
y
=
)-
y = 3 + 3 cos
*-
y
=
3 sen x ,!2 " # x # 2 "
" ! x % ,(4 ) x ) 4 $# 2 ' & " x % 4 ! 2 cos $ ' ,!4( ) x ) 4 ( # 2 &
HK- b% #*%*3&);3 )* 4;33$*%5* &:5*3%& #*%*3& 9%& 4;33$*%5* )&)& C;3
I
=
(
)
30 sen 120t
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()
f x 1$
B
()
5&:*= L9*0
( ) ( B 1) ! Bsen ( x )
sen x
g x
*= 9% %^2*3; 3*&: C;=$5$@;Q *: @&:;3 )*
/9%4$U% &74)*-
=
g : ! " !
B
=
+
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( g ! f ) =*& (JQ )*7* =*3 $#9&: &0
J K M (I (, ?*=C9*=5&0 7-
HN- [;=L9*D* :& #3"/$4& )* :& /9%4$U%0
()
g x
=
4!
1 2
"
cos $ 2 x !
#
% ', 2&
!
x
( )*!2! ,2! +,
!"#$%& K )* +,
IR- 1$ *: @;:5&D* 1 60
E *%
9% 4$349$5; *:E453$4; 5$*%* 9%& &2C:$59) )* ((R @;:5$;= A 9% C*3T;); )*
=*#9%);=Q A =$
/;32& E
=
E
=
110 volts
49&%); t
=
0 seg .Q
*%49*%53* 9%& *49&4$U% )* :&
( ) L9* *%53*#9* *: @;:5&D* C&3& 49&:L9$*3 @&:;3 )* t ! 0 6
Acos Bt
?*=C9*=5&0 E
=
(
)
110 cos 120t
I(- X% :;= C3;7:*2&= =$#9$*%5*=Q )*5*32$%* :& *49&4$U% )* :& /;32& y Asen( Bx ) Q L9* =
C3;)9_4& :& #3"/$4& 2;=53&)&6 &-
7-
4-
)-
?*=C9*=5&0 &4-
y
I+- [;=L9*D* :& #3"/$4& )* :& /9%4$U% f : !"!4 , 4 #$ f ( x )
=
2e
( )
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( ) Q 7- y !10 sen ( x ) Q )- y
y
=
=
3 sen 4 x !
=
=
( )Q !0.5 sen (0.5 x )
0.25 sen 0.25 x !
49A& 3*#:& )* 4;33*=C;%)*%4$& *=
6 .*=43$7& :&= 4&3&45*3T=5$4&= )* *=5& /9%4$U%0 $%A*45$@&Q =;73*A*45$@&Q
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)
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()
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=
( ( ))
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( ( ))
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e
x
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3 2
+
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1 3
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T
A :& &2C:$59)
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/9%4$U%Q A #3&/$L9* C&3&
1 x
=
( )6 X>C3*=* *:
cos 8t
3
0 " t " ! 6
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19 3*#:& )* 4;33*=C;%)*%4$& *=0 &-
()
f x
7- f ( x ) 4-
()
f x
=
=
( ( ))
µ sen 2 x
( ( ))
µ tan 2 x
( ( ))
µ csc 2 x
( ( )) f ( x ) µ ( sec (2 ))
)- f ( x ) *-
=
=
µ cot 2 x
=
x
?*=C9*=5&0 &-
()
IM- [;=L9*D* :& #3"/$4& )* :& /9%4$U%0 f x
()
IN- [;=L9*D* :& #3"/$4& )* :& /9%4$U%0 f x
,R- [;=L9*D* :& #3"/$4& )* :& /9%4$U%0 f ( x )
=
() ()
( ( ))
sgn cos 2 x
! ! $$ # sen x & , # && # # " 2 %&% "
=
,(- [;=L9*D* :& #3"/$4& )* :& /9%4$U%0 f x ,+- [;=L9*D* :& #3"/$4& )* :& /9%4$U%0 f x
=
=
=
x
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2
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( ) ( ) csc ( x ) sen ( x )
tan x ! sen x
(R,- !&3& L9* :& *>C3*=$U%
4
)*7* 492C:$3=* L9* ! =*& $#9&: &0 &- sec x 7- cos x 4-
( )
()
=
sen
"
=*& 9%& $)*%5$)&) 53$#;%;2E53$4&Q
( )
1 + cos x
()
)-
x
csc
( )
*-
x
tan
() x
?*=C9*=5&0 &(RJ- .* =*3 C;=$7:*Q )*29*=53* L9*0
( ) ! tan(35º )
tan 55º
=
(
)
2tan 20º
" cos (RK- P;%=$)*3&%); :&= 3*=53$44$;%*= )*: 4&=;Q :& *>C3*=$U% $1 ! $# *L9$@&:*%5* &0
(2 sen ( 2 tan ( 2 cot ( 2 csc ( 2
&-
cos
2
2
7-
2
4-
2
)-
2
*-
2
( ) ! sen ( ) % ' sec ( 2 ) '& 2
x
x
*=
x
) ) ) ) )
x
x
x
x
x
?*=C9*=5&0 7@A9 !NDMNLFBJG J LBJNDMNLFBJG OPLCFBFIQOPLNMG (RM- 1*& *: 4;%D9%5; 3*/*3*%4$&: Re
=
!"0, $# A *: C3*)$4&); p ( x ):
()
O& =92& )* :;= *:*2*%5;= )*: 4;%D9%5; )* @*3)&) Ap x &-
0
7-
4
4-
2
)-
1
=
sen
2
() x
*= $#9&: &0 *-
2
?*=C9*=5&0 4!"#$%& (N )* +,
(RN- 1*& Re
=
(0,2 ) A p ( x )
: sen
() x
( ) 6 .*5*32$%* Ap ( x ) 6
cos x
=
" ! 5! % & $4 4 '
?*=C9*=5&0 # ((R- 1*& Re !"0, #$ A =
()
p x : 2cos
2
( )! x
sen
(2 ) x
=
06
,
()
.*5*32$%* Ap x 6
"! !% & 4 2 $ '
?*=C9*=5&0 #
,
(((- 1*& *: 4;%D9%5; 3*/*3*%4$&: Re !"0 ,4! #$ A *: C3*)$4&); )* 9%& @&3$&7:*0 =
()
p x :
cos
2
( x)
+ sen
2
!x$ 1 # &= "2% 2
()
S&79:* *: 4;%D9%5; )* @*3)&) Ap x 6
()
?*=C9*=5&0 Ap x
((+- 1$ Re
=
=
#$ !" ,2" %& Q )*5*32$%* *: 4;%D9%5; )* @*3)&) )*: C3*)$4&);0
( )
p !
=
( )
tan 2!
+
( )
2 cos !
?*=C9*=5&0 Ap ( ! ) ((H- 1*& Re !"0, #$ A $#9&: &0 =
&-
! ! ! 3! 5! 7! 5! 7! 11! $ " , , , , , , , % #3 2 2 3 3 2 2 3 &
()
7-
0
( )!2 ( )
p x : tan 2 x
!
sen
4-
3
x
=
0 6
0
$ # # 5# # 7 # 3# 11# ' %" ," ," , , , , ( & 2 6 6 2 6 2 6 )
()
O& =92& )* :;= *:*2*%5;= )* Ap x *=
)-
!
=
=
5!
*-
3
7! 3
?*=C9*=5&0 )((I- 1*& Re
=
"#0 ,2 ! $% A *: C3*)$4&);
( )
( )
( ) 6 .*5*32$%* *: 4;%D9%5;
p x : sen 2 x = 1 + cos 2 x
)* @*3)&) Ap ( x ) 6 ?*=C9*=5&0 Ap( x )
((,- 1*& *: 3*/*3*%4$&: Re
( )
p ! : 1 "
( )
2 cos x
=
=
=
&' ' 5' 3' # % , , , " $4 2 4 2 !
"#0 ,4! ) Q )*5*32$%* *: 4;%D9%5; )* @*3)&) )*: C3*)$4&);
0
&' 7' 9' 15' # , , " 4 4 4 4 ! $
?*=C9*=5&0 Ap(( ) % , =
((J- 1*& *: 4;%D9%5; 3*/*3*%4$&: Re !"0,2! #$ A *: C3*)$4&);0 =
()
p x :
2 cos
2
() x
=
1 ! sen
() x
.*5*32$%* :& =92& )* :;= *:*2*%5;= )* Ap ( x ) 6 !"#$%& +R )* +,
((K- 1*& *: 4;%D9%5; 3*/*3*%4$&: Re
( ) q( x) :
p x :
( ) sec ( 2 x ) cot 2 x
=
=
"#0,! $% A :;= C3*)$4&);= )* 9%& @&3$&7:*0
1
2
=
!
\)*%5$/$L9* :& C3;C;=$4$U% FX?.].X?]0
( ) 7- N ( Ap ( x ) Aq ( x )) 4- N ( Ap ( x ) Aq ( x )) )- N ( Aq ( x ) ! Ap ( x )) *- N ( Ap ( x ) Aq ( x )) &- N Ap ( x ) ! Aq ( x )
=
1
!
=
!
=
0 2
=
!
4
=
2
?*=C9*=5&0 &((M- ?*=9*:@& C&3& x *% *: $%5*3@&:; $%)$4&);0 &-
( )
1 + cos x
= 0 ,x
! #$0 ,2 " ) ?*=C9*=5&0
x
=
!
7- 1 ! sen ( x ) = 0 ,x " ! Q +
?*=C9*=5&0 x
4-
1+
( )
2 sen x
= 0 ,x
! =
( 4n 3) ;n "
2
#!
! #$ 0 ,2 " ) ?*=C9*=5&0
x
& 5( 7( # '% , " $4 4 !
((N- ?*=9*:@& C&3& x *% *: $%5*3@&:; $%)$4&);0 &-
2
( )!3
4 cos x
=
0 ,x " $ %0 ,2 #
) &( 5( 7( 11( # , , " $6 6 6 6 !
?*=C9*=5&0 x ' % ,
7-
2
( )
2 sen x
!1=
0 ,x " !
+
?*=C9*=5&0
4-
( )
2 cos 2 x
=
1 ,x ! # $0 ,2 "
x
&( 3( 5( 7( # ' % , , , ,!" $4 4 4 4 !
) &( 5( 7( 11( # , , " 6 6 6 6 ! $
?*=C9*=5&0 x ' % ,
)-
( )
2 sen 2 x
=
3 ,x
!!
+
&( ( 7( 4( # , , ,!" $6 3 6 3 !
?*=C9*=5&0 x ' % ,
!"#$%& +( )* +,
()
(+R- 1$ Re "#!! ,2! %$ A
( )!2 ( )
p x : 2 sen 2 x
=
( ) !1
sen x + 2cos x
=
0Q
)*5*32$%* *: 4;%D9%5; )*
()
@*3)&) Ap x 6 (+(- 1*& Re !"0,2 #$ A =
()
p x : 2 sen
2
() x
=
1 ! cos
( ) *%5;%4*= :& =92& )* :;= *:*2*%5;= )* x
()
Ap x *= $#9&: &0 &-
8
7-
3
4-
3
4
)-
3
*-
4
7 3
?*=C9*=5&0 )(++- 1$ Re !"0,2 ! $# A =
()
p x :
sen
(2 ) cos ( ) x
x
=
6 sen
3
( ) Q )*5*32$%* :& =92& )* :;= *:*2*%5;= )*: x
()
4;%D9%5; )* @*3)&) Ap x 6 (+H- 1$ Re "#!! ,2! %$ A =
()
( )!2 ( )
p x : 2 sen 2 x
sen x
( ) !1
+ 2cos x
=
0Q
)*5*32$%* *: 4;%D9%5; )*
()
@*3)&) Ap x 6
()
?*=C9*=5&0 Ap x
(+I- 1$ Re !"0,1$# A =
p
(! ) :
(
)
3 ! 3 sen 2!"
=
2cos
2
=
" 5! ! ! ! 7! 5! 11! % #! , ! , ! , , , , & $ 6 3 6 3 6 3 6 '
(2!" ) Q )*5*32$%* *: 4;%D9%5; )* @*3)&)
Ap ( ! ) 6 (+,- 1*& *: 3*/*3*%4$&:
Re
=
"#0 2 ! %$ A *: C3*)$4&); p ( x ) : ,
( )!
sen 2 x
( )
2cos x
=
0 6
()
X%5;%4*=Q :& =92& )* :;= *:*2*%5;= )*: 4;%D9%5; )* @*3)&) Ap x *=0 &74)*-
!
3! 4 5! 4
3!
0
?*=C9*=5&0 )(+J- 1*& Re
=
(
0,2
)
A p ( x ) :
( )
sen x >
1 2
()
6 .*5*32$%* Ap x 6
! !
?*=C9*=5&0 #
"6
5! $ ,
6
& %
!"#$%& ++ )* +,
(+K- 1*& Re
=
(0,2 ) A p ( x ):
1
( )
cos x <
3
()
6 .*5*32$%* Ap x 6
! !1$ ! 1 $$ ?*=C9*=5&0 # arccos # & ,2! ' arccos # && " 3% " 3 %% " (+M- 1$ Re
=
#$ !" ," %& Q )*5*32$%* *: 4;%D9%5; )* @*3)&) )*: C3*)$4&);0
( ( ) )
( )
p ! : µ sen 2! " 1 < 0
?*=C9*=5&0 Ap ( !) (+N- 1*& Re !"0,2 #$ A
()
p x
=
"
: sgn $ sen
#
() ( x
cos
x
=
"
1 % ! ) 4 '& 0 *%5;%4*= :& =92& )* :;= =
()
*:*2*%5;= )* Ap x *= $#9&: &0 &-
7-
12
4-
2
)-
2
*-
3
?*=C9*=5&0 *(HR- 1$ Re "#!2! ,2! %$ A =
p
( ) : µ ( !
sen 2!
)
=
?*=C9*=5&0 Ap
(H(- 1*& *: 4;%D9%5; 3*/*3*%4$&: Re
()
)* @*3)&) Ap x
() !
)*5*32$%* *: 4;%D9%5; )* @*3)&) Ap =
() !
" " ! % " 3! % ! % 3! % " ! ! ! ! ( ! ! ( ( 2 , , 0 $ ' $ ' { } $ , ! ' ( $ ,2! ' 2 2 # & # & #2 & # 2 &
(0,2 ) A *: C3*)$4&); p ( x):
()
cos x
1 >
2
6 X: 4;%D9%5;
*= $#9&: &0
!
$ ! 11 ,2 &'# 6 6 " % " ! $ !5 7- # 0, & ' # ,2 " 3% " 3 ! 5 $ 4- # , & "3 3 % ! 11 $ )- # , & "6 6 %
$ & %
&- # 0,
*-
=
0Q
$ & %
!
?*=C9*=5&0 7(H+- 1$ Re
=
#$ !" ," %& Q )*5*32$%* *: 4;%D9%5; )* @*3)&) )*: C3*)$4&);0
( )
! #"
p x : sgn sen
! x $ $ ' 1 #" 2 & % & % ?*=C9*=5&0 Ap ( x ) = { x
}
0 < x ! "
!"#$%& +H )* +,
(HH- 1*& *: 4;%D9%5; 3*/*3*%4$&: Re !"0 ,2! #$ A *: C3*)$4&); )* 9%& @&3$&7:*0 =
(
()
( ))
3 ! 2 cos x
µ
p x :
=
0
()
.*5*32$%* *: 4;%D9%5; )* @*3)&) Ap x 6
()
?*=C9*=5&0 Ap x
! 3! $ & A :;= C3*)$4&);= " 2%
(HI- 1*& *: 4;%D9%5; 3*/*3*%4$&: Re # 0, =
()
()
q x :
cos x
<
( ()
(H,- 1*& *: 4;%D9%5; 3*/*3*%4$&: Re
( ) (
( ))
=
!
()
p x :
( )
sen 2 x
>
0
A
( )) 6
q x
"#0 ,2! $% A :;= C3*)$4&);=
=
( )
p x
! " x % $& # ! : #1 2cos $ ' & A # # 2 & &% "
0 6
( ()
.*5*32$%* *: 4;%D9%5; )* @*3)&) A p x
!
( )) 6
q x
?*=C9*=5&0 A[ p ( x ) ( q( x )]
(HJ- 1$ Re !"0,2 $# A *: C3*)$4&); =
@*3)&) Ap
! ! $ !11! $ , , ' 0 2 ! # & # & " 6% " 6 %
06
.*5*32$%* *: 4;%D9%5; )* @*3)&)0 A p x
q x : sgn 2 x
=
()
p ! :
sen
(!" ) cos (!" )
1 !
4
=
[0, ) ) ' &$
4)
% 3
# "
,2) !
Q )*5*32$%* *: 4;%D9%5; )*
(! ) 6 ?*=C9*=5&0 Ap
(HK- 1$ Re !"0, ! $# A =
()
p x :
sen
(2 )
( ) !
()
x + sen x
=
! 1 $ ! 5 7 $ ! 11 13 $ !17 19 $ ! 23 $ #0, & ' # , & ' # , & ' # , & ' # ,2& " 12 % "12 12 % "12 12 % "12 12 % "12 %
>
( )
cos 2 x
( )Q
+ cos x
)*5*32$%* *: 4;%D9%5; )*
()
@*3)&) Ap x 6
()
?*=C9*=5&0 Ap x
=
! ! 5! $ # , & "6 6 %
(HM- 1*& *: 4;%D9%5; 3*/*3*%4$&: Re !"0 ,3! #$ A *: C3*)$4&); )* 9%& @&3$&7:*0 =
()
q x :
! 2 x $ & <1 " 3%
2 cos #
()
.*5*32$%* *: 4;%D9%5; )* @*3)&) Aq x 6
()
?*=C9*=5&0 Aq x
=
! ! 5! $ # , & "2 2 %
!"#$%& +I )* +,
(HN- 1*& f : X ! " 9%& /9%4$U% )* @&3$&7:* 3*&: 49A& 3*#:& )* 4;33*=C;%)*%4$& *=0
()
f x
"
=
()
1 %
()
ln $ sen x cos x ! '
#
X=C*4$/$L9* 49": )*7*3T& =*3 *: 4;%D9%5; $ X ! " #0,2 ! % 6
X
4&
2"= &)*49&); A L9* 492C:& *=5& 4;%)$4$U%
?*=C9*=5&0 X
=
" ! 5! % " 13! 17 ! % , ( $# 12 , 12 ' & $# 12 12 ' &
(IR- 1*& f : X ! " 9%& /9%4$U% )* @&3$&7:* 3*&: 49A& 3*#:& )* 4;33*=C;%)*%4$& *=0
()
f x
1
=
1 + sen
X=C*4$/$L9* 49": )*7*3T& =*3 *: 4;%D9%5; $ X ! " #0,2 ! % 6
( x) ! 2 cos ( x )
X
2
2"= &)*49&); A L9* 492C:& *=5& 4;%)$4$U%
?*=C9*=5&0 X
=
" ! 5! % $# 6 , 6 ' &
!"#$%& +, )* +,
