Download 7.6 Power Point

7.6 – The Inverse Trigonometric
Ratios
Essential Question: How do you
make a function without an inverse
have an inverse?
• From chapter 4, we learned that for
a function to be one-to-one and
have an inverse it must pass the
horizontal line test.
• If you look at the tangent graph, the
graph of tan x is not one-to-one, so
therefore has no inverse.
• However, if we restrict our domain,
like in the second picture, it is oneto-one and thus has an inverse.
Tangent Graph
The inverse is the third picture and is denoted:
f -1(x) = Tan -1 x
Example
Find Tan -1 3 with a calc in a) degrees and b) radians.
The inverse of the sine and cosine graphs:
Pictures:
Example:
Find with calc:
a. Sin
-1
3
8
b. Cos -1 (-.2)
Example:
Find without using a calc:
a. Tan -1 (–1)
b. Tan -1 (1)
c. Sin
-1
2
2
d. Cos

2


-1  

 2 
Examples:
- Find sec (Tan
-1  1
3
) with a calc.
4
- Find csc (Cos (
)) using a graph
5
(without a calc.).
-1
Example:
- Find the approximate value and exact value
of csc (Cos -1 ( - .4)).