Math 151
Section 4.6
Inverse Trig Functions
y = arcsin x = sin!1 x
y = arccos x = cos!1 x
y = arctan x = tan!1 x
Example: Find the exact value of the expression:
" 3 %'
$
A. sin!1 $$ ''' =
$# 2 '&
" 1%
B. sin!1 $$! ''' =
$# 2 '&
" 2 %'
$
C. cos!1 $$ ''' =
$# 2 '&
" 1%
D. cos!1 $$! ''' =
$# 2 '&
( )
E. tan!1 ! 3 =
! 5! $
F. arcsin ##sin &&& =
#"
4 &%
Math 151
! 5! $
G. arccos##cos &&& =
#"
4 &%
! 7! $
H. arctan ## tan &&& =
#"
4 &%
Example: Find the exact value of the expression:
"
" 1 %%
A. cos$$$sin!1 $$ '''''' =
$# 2 '&'&
$#
"
2%
B. sec $$ tan!1 ''' =
$#
3 '&
C. sin ( tan!1 ( x)) =
D. cos(sin!1 ( x)) =
Math 151
Derivative of Inverse Trig Functions
d
1
sin!1 x =
dx
1! x 2
d
1
tan!1 x =
dx
1+ x 2
d
1
sec!1 x =
dx
x x 2 !1
d
!1
cos!1 x =
dx
1! x 2
d
!1
cot!1 x =
dx
1+ x 2
d
!1
csc!1 x =
dx
x x 2 !1
Example: Find the derivative.
A. y = (sin!1 (2x ))
2
B. y = cos!1 (4x 2 )
C. y = arctan (sin (4x))
D. y = x sec
!1 x