Download Inverse Sine Function

Class Work
1. Find the exact value of cot 330
2. Find sin2x, cos2x, and tan2x given
tan x = -3/2 and 90 < x< 180
Class Work
u
2
3. Find sin given sin u   and 180 < x < 270
2
3
Section 7.4
Inverse Trigonometric Functions
Objectives:
•To define the inverse of the sine,
cosine, and tangent functions.
•To understand the domain and range
of the inverse trig functions.
Inverse Sine Function
The inverse of the function sin is the function
sin–1 defined by:
sin–1x = y

sin y = x
for –1 ≤ x ≤ 1 and –π/2 ≤ y ≤ π/2.
Example 1. Find the exact value of the
expression if it is defined:
(a)sin–1 ½
(b)sin–1 (–½)
(c)sin–1 (3/2)
Class Work
Find the exact value of the expression if it is
defined:
4.


1  2
sin 

 2 
5.
5
sin
4
1
Inverse Cosine Function
The inverse cosine function is the function
cos–1 with domain [–1, 1] and range [0, π],
defined by:
cos–1 x = y

cos y = x
Ex 2. Find the exact value of the expression if it
is defined:
(a) cos–1 ( 3 / 2)
b) cos–1 0
c) cos–1 (5/7)
Class Work
Find the exact value of the expression if it is
defined:
6. cos 1 2
2
1
7. cos (1)
Inverse Tangent Function
The inverse tangent function is the function tan–1
with domain and range (–π/2, π/2) defined by:
tan–1 x = y

tan y = x
Ex 3. Find the exact value of the expression if it
is defined:
(a) tan–1 1
(b) tan–1 3
(c) tan–1(–20)
Class Work
Find the exact value of the expression if it is
defined:
8.
9.
1
tan (1)
tan
1
3
3
Ex 4. Find the exact value of the expression, if it
is defined.
a.)
b.)
1

sin (sin )
4
1
tan(tan 5)

  
c.) cos  cos    
 3 

1
Class Work
Find the exact value of the expression, if it is
defined.
  
10.sin  sin 
  6
1



2 

11. tan  tan

3 

1
Ex 5. Find the exact value of the expression, if it
is defined.
a.) sin 1  cos 2 


3


 1 1 
b.) tan  sin

2

5 

c.) sin  cos 
6 

1
Class Work
Find the exact value of the expression, if it is
defined.
 1 1 
12. tan  sin

2

13. cos 1  sin 3 


4


HW#4 p557
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