Inverse Trigonometric Functions

1
Inverse Trigonometric Functions

• Section 4.7

2
Objectives

• Evaluate inverse trigonometric functions at given
  values.
• State the domain and range of each of the inverse
  trigonometric functions.
• Use right triangles to find the composition of a
  trigonometric function and an inverse
  trigonometric function.
• Solve simple trigonometric equations requiring
  inverse trigonometric functions.

3
Vocabulary

• arcsine of a number
• arccosine of a number
• arctangent of a number
• arcsecant of a number

4
The graph of the function f(x) sin(x) is not
one-to-one
5
The restricted graph of the function f(x)
sin(x) is one-to-one
6
and thus has in inverse function
What is the domain?  What is the range? 
7
The graph of the function f(x) cos(x) is not
one-to-one
8
The restricted graph of the function f(x)
cos(x) is one-to-one
9
and thus has in inverse function
What is the domain?  What is the range? 
10
The graph of the function f(x) tan(x) is not
one-to-one
11
The restricted graph of the function f(x)
tan(x) is one-to-one
12
and thus has in inverse function
What is the domain?  What is the range? 
13
Evaluate each of the following (remember that the
output of an inverse trigonometric function is an
angle)
What angle between and has a sine
value of 1?
What angle between and has a sine
value of -1/2?
What angle between 0 and p has a cosine value of
0?
14
Evaluate each of the following (remember that the
output of an inverse trigonometric function is an
angle)
What angle between and has a
tangent value of ?
What angle between and has a sine
value of ?
What angle between 0 and p has a cosine value of
-1?
15
Evaluate each of the following
16
Evaluate each of the following
17
Evaluate each of the following
18
Rewrite the expression as an algebraic expression
in x