Inverse Functions

1. Unit 2 – Learning Goal 1 Inverse Functions

2. Transition #1 – Before and After • Official Name of our high school where Jack Black is a substitute teacher. • The exact value of sin(4π/3)equals Harper Lee’s Pulitzer Prize-winning novel • Member of “Wham!” who recorded “Thriller” • Neil Patrick Harris’ TV show about a Nobel Peace Prize-winning nun who founded the Missionaries of Charity

3. Functions & Inverse Functions • Have 2 main properties: • 1) Points are interchanged: • Function has points: (A, B) and (C, D) • Inverse has points: (B, A) and (D, C) • 2) Cancel each other: • f(f -1(x)) = x

4. Inverse Trig Functions Function Inverse Symbol sine arcsine arcsin or sin-1 cosine arccosinearccosor cos-1 tangent arctangent arctanor tan-1

5. Inverse Trig Functions Things to Remember about Inverse Trig functions or “arc”-functions 1) “arc” functions equal theangle 2) “arc” functions give you the coordinate, want you to find the angle 3) “arc” functions are not defined around the whole circle

6. Inverse Trig Functions Inverse Function Defined from: arcsine sin θ = y arccosine cosθ =x arctangent tan θ = y/x

7. Inverse Trig Applications Find the value for x. 24 x 26

8. Solution • Since we have the opposite side and an adjacent side to our angle x, we can use the tangent function to write an equation: • tan x = 24/26 • tan x = .923077 • tan-1( tan x )= tan-1(.923077) • x= tan-1(.923077) • x= .7454 radians or 42.7°

9. Re-writing Trig and Inverses sin θ = kcan be re-written as sin-1k=θ cosθ = kcan be re-written ascos-1k = θ tan θ = kcan be re-written astan-1k = θ

10. Evaluating Inverse Functions

11. Name that tune – Movie Themes • Movie #1 – 1993 • “Jurassic Park” • Song #2 – 1991 • “Terminator 2” • Song #3 – 1969 • “The Good, the Bad, and the Ugly” • Song #4– 2011 • “True Grit”