argsinh( )x argcoth( )x argtanh( )x =argtgh( )x sin( )x cos( )x tan( )x

funct f
sin(x)
π
2
ix −ix
= e −e
2i
1
−1
odd, T= 2π
cos( x)
=
sin(x+y)=sin( x)cos( y)+cos( x)sin( y)
3π
2
π
2
2π
π
1
π
2
3π
2
π
2π
π
2
π
2
π
D( f )=IR
3π
2
2π
D( f ): x = π2 +kπ
π
2
π
2
3π
2
π
2π
D( f ): x =kπ
x −x
= e −e
2
odd
D( f )=IR
cosh(x)
x −x
= e +e
2
1
f dx =
−cos(x) D( f−1)=[−1,1]
−sin(x) arccos( x )
cot( x)cot( y)−1
cot( x)+cot( y)
f dx =
sin( x)
graph f−1
1
2
cos (x )
1
1−x 2
π
2
−1
1
π
2
D( f−1’)=(−1,1)
−1
1−x 2
π
D( f−1)=[−1,1]
arctan(x)
=arctg(x)
−1
coth(x)
1
−1
π
2
D( f−1)=IR
arccot(x)
2
2
cosh ( x)−sinh ( x)=1
D( f−1’)=(−1,1)
1
x2+1
D( f−1’)=IR
−1
x2+1
π
π
2
D( f−1)=IR
D( f−1’)=IR
1
x 2 +1
cosh(x) argsinh(x)
=ln(x+ x2+1 )
f dx =
cosh(x) D( f−1)=IR
sinh(x) argcosh(x )
cosh( x+ y)=cosh(x)cosh( y)+sinh( x)sinh( y)
2
2
2
cosh(2 x)=cosh ( x)+sinh ( x)
f dx = =ln(x+ x −1 )
2
cosh(2 x)+1
D( f )=IR cosh ( x)=
sinh(x) D( f−1)=[1, )
2
1
x)+tanh( y)
argtanh(x )
tanh( x + y)= tanh(
2
1+tanh( x)tanh( y)
cosh (x ) =argtgh(x)
x
tanh(2 x)= 2tanh(2 x)
= 12 ln(1+
1−x)
f
dx
=
1+tanh ( x)
ln|cosh(x)| D( f−1)=(−1,1)
D( f )=IR
−1
1+coth( x)coth( y)
argcoth( x)
coth( x +y)=
2
y
coth( x)+coth( )
sinh (x )
= 12 ln( x+1
2
x−1 )
1+coth ( x)
coth(2 x)=
2coth( x)
D( f ): x =0
D( f−1): | x|>1
D( f−1’)=IR
1
x 2 −1
1
D( f−1’)=(1, )
1
1−x2
8
1
π
2
2
cot ( x)−1
cot(2 x )=
2 cot( x)
1
−1
f dx =
−ln|cos(x)|
−1
2
sin (x )
f−1’
π
2
8
even
odd
cos ( x)= 1+cos(2 x)
2
sinh( x +y)=sinh( x)cosh( y)+cosh( x)sinh( y)
sinh(2 x)=2sinh( x)cosh( x)
2
sinh ( x)= cosh(2 x)−1
2
sinh(x)
cosh(x)
2
tan( x)+tan( y)
1−tan(x)tan( y)
tan(2 x )= 2 tan(2 x)
1−tan (x)
cot( x+ y)=
odd, T=π
= sinh(x)
2
cos(2 x)=cos ( x)−sin (x)
tan( x + y)=
odd, T=π
odd
sin( π2 )= 24 =1 sin2(x)+cos2( x)=1
2
π
2 −1
even, T=2π
tanh(x)
=tgh(x)
sinh( x)
= cosh(
x)
sin( π3 )= 23
2
sin (x)= 1−cos(2 x)
2
f ’ f inverse f−1
cos(x) arcsin(x)
cos( x + y)=cos( x )cos( y)−sin(x)sin( y)
2
cot(x)
cos( x)
= sin( x)
sin(2 x)=2sin(x)cos( x)
D( f )=IR
sin(0)= 20 =0 sin( π6 )= 21 = 12 sin( π4 )= 22
eix+ e−ix
tan( x)
=tg( x)
sin(x)
= cos(
x)
identities
graph (with 1−1 restriction)
1
−1
D( f−1’)=(−1,1)
1
1−x2
−1
1
D( f−1’): | x|>1
c pHabala 2009