1. The Inverse Trigonometric Functions
Section 7-6
The Inverse Trigonometric Functions

2. The Inverse of Tangent
From the graph of f(x) = tan x shown on p. 287, we can see that the tangent function is not one-to-one and has no inverse. But, if we restrict x to the interval , the restricted function, which we denote F(x) = Tan x, is one-to-one. Its inverse is denoted and is read “the inverse tangent of x.” Notice that means that tan y = x and

3. Inverse Tangent
Why does tangent have an inverse in Quadrants 1 and 4 only?
Why are not included?

4. The Inverse of Sine
By considering only the solid portion of the graph of g(x) = sin x, as shown on p. 287, we obtain a new function G(x) = Sin x with domain This graph has an inverse
, whose graph is shown on p Note that means that sin y = x and

5. Inverse Sine
Why does sine have an inverse in quadrants 1 and 4 only?

6. The Inverse of Cosine
By considering only the solid portion of the graph of h(x) = cos x, as shown on p. 288, we obtain a new function H(x) = Cos x with domain 0 < x < π. This graph has an inverse , whose graph is shown on p Note that means that cos y = x and 0 < y < π.

7. Inverse Cosine
Why does cosine have an inverse in Quadrants 1 and 2?

8. Example
Use a calculator or table to find the value of each expression to the nearest tenth of a degree and to the nearest hundredth of a radian. b. c.

9. Example
Without using a calculator or table, find the value of each expression in radians.
b. b. c.

10. Example
Evaluate each expression without using a calculator

11. Example
Find an approximate value and the exact value of csc ( (-0.4))