Mathematical Investigations IV
Name:
Mathematical Investigations IV
Trigonometry - Beyond the Right Triangles
Inverse Trig Functions
For all problems, find all values in radians, giving exact values wherever possible. Use your calculator only to
check answers as necessary.
Let’s recall a few things about inverse functions
Analytically, if functions ƒ and g are inverses,
then
Graphically, if functions ƒ and g are inverses,
then
Functions have inverses that are functions if and only if they are one-to-one. What does it mean
to say that a function is “one-to-one”?
1.
Now consider the inverse trig functions and sketch the following.
y = sin x
the relation x = sin y
State the domain and range of y  sin 1 (x) .
Sketch part of the graph of x = sin y above
to create the inverse function y  sin 1 (x) .
Domain:
Range:
(Verify your graph with your calculator.)
I
Trig. 6.1
Rev. S06
Mathematical Investigations IV
Name:
2.
Find the exact value (without using your calculator!) of the following, keeping in mind
the domain and range of y  sin 1 (x) determined on the previous page.
 3
sin 1 

 2 
3.
 1
sin 1  
 2
sin 11
 2
sin 1 

 2 
Sketch the graph of y = cos1 (x) , marking the scale clearly on each axis.
State the domain and range.
Domain:
Range:
4.
Find the exact value of the following, without using your calculator. (Don’t forget about
domain and range.)
 2
cos1 

 2 
5.
cos11
1 
1
cos  
 2
 3
cos 1 

 2 
Sketch the graph of y = tan 1 (x) , marking the scale clearly.
State the domain and range.
Domain:
Range:
6.
Find the exact value of the following.
tan-1 (1)
I
tan1
tan-1 (-1)
Trig. 6.2

3
 3
tan 1  
 3 
Rev. S06
Mathematical Investigations IV
Name:
7.
Find exact values for each of the following. (No calculators!)

1
b.
 3 
sin 1sin  
  2 
 3 
tan 1tan  
  4 
d.
   
cos1cos 
  4 
e

4
sin cos1 
5

f.

2
sin tan 1 
3

g.
cos sin
h.
tan cos
a.
sin sin
c.

1
a
1

a
1
2
, find the value of sin(x).
3
8.
Given tan(x) 
9.
Solve each equation over the given domain. Give answers to the nearest hundredth of a
degree.
2
2
a.
tan(3x + 4) = for 0 < x < 90o
b.
tan(3x + 4) =  for 0 < x < 180o
3
3
I
Trig. 6.3
Rev. S06