1. 1.9 Inverse Trig Functions Obj: Graph Inverse Trig Functions
Trig / Precalculus
1.9 Inverse Trig Functions
Obj: Graph Inverse Trig Functions

2. Review Inverse Functions
If f(x) = 3x + 4, find f-1(x). Find f-1(f(x)). What are the domain and range? If f(x) = x2 + 2, find f-1(x). What are the domain and range? If f(x) = sin x, find f-1(x).

3. Definition
Suppose f is a one-to-one function with domain A and range B. The inverse function f-1 is a function with these properties: 1) f-1 has domain B and range A 2) f(f-1(x)) = x

4. Periodic Functions
Consider the 3 periodic functions we discussed last class. Is f(x) = sin x a one-to-one function? y = cos x? y = tan x?

5. Graphs
Graph y = sin x from -360⁰ < x < 360⁰. Graph y = sin-1 x from -360⁰ < x < 360⁰. Reduce the domain to -90⁰ < x < 90⁰ and repeat.

6. Equations Solve the following equations. sin 30⁰ = x sin-1x = ½
Simplify.
sin(sin-1(1/2))
sin(sin-1(1))

7. Cosine Graph y = cos x from -360⁰ < x < 360⁰.
Reduce the domain to -90⁰ < x < 90⁰.
Is the function one-to-one?
How should the domain be reduced?
Graph y = cos-1x.

8. Tangent Graph y = tan x from -360⁰ < x < 360⁰.
Reduce the domain to -90⁰ < x < 90⁰.
Is the function one-to-one?
Graph y = tan-1x.

9. Equations 3 sin x + 7 = 5 5 cos x – 12 = 14 2 tan x + 3 = -10
no solutions
2 tan x + 3 = -10
x = ’14”
10 cos (x + 3) – 7 = 13

10. Using Triangles Find cos(sin-1(7/25)).
In words, “What is cosine from the angle at which sine is 7/25?”
Label the sides.
Find cosine.

11. Assignment
1.9 page 48 5, 7,