Transcript 4.7 Inverse Trigonometric Functions

4.7
Inverse Trigonometric
Functions
Definition of the Inverse Trig. Functions
1.
arcsin x
quadrants I and IV
2.
arccos x
quadrants I and II
3.
arctan x
quadrants I and IV


2
 y

2
0  y 



2
 y
2
3
Find the values of :
 1
arcsin   
 2
-1
I or IV
2
 30 or 
sin
1
3
2
I or IV
60 or
2
3

3
1

6
2
arccos
2
I or II
45 or

2
4
1
arccos1
180 or 
0
1
-1
1
Use your calculator to approximate the value.
Calculator in radians.
arctan( -8.45 )
-1.453001
arcsin( 0.2247 )
.226635
arccos( 2 )
error
Remark: the domain of the inverse functions
of cosine and sine are [-1,1].
Use an inverse trig.
function to write 
as a function of x.
x
cos 
5
x 
arccoscos   arccos 
5 
x 
  arccos 
5 
x

5
Find the exact value.
1
tan[arctan(-5)]
-5
What is the tan of
this triangle? -5
 5 
arcsin  sin

3 

5
3
   

arcsin  sin      
3
  3 
is coterminal to what
angle that is in the
domain of arcsin?


3
Find the exact value.
2

tan  arccos 
3

opp
5


adj
2
3
5
2

 3 
cos arcsin   
 5 

adj 4


hyp 5
4
5
-3
Find sin(arccos 3x)
1
0 x
3
1 = (3x)2 + b2
1
?=
3x
sin(arccos 3x)
cot(arccos 3x) 
1  9x  b
2
opp
1  9x


hyp
1
3x
1 9x2
2