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

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).

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

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?

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.

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

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.

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.

Equations 3 sin x + 7 = 5 5 cos x – 12 = 14 2 tan x + 3 = -10 no solutions 2 tan x + 3 = -10 x = -81015’14” 10 cos (x + 3) – 7 = 13

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.

Assignment 1.9 page 48 5, 7, 9 - 14