# Inverse Functions - PowerPoint PPT Presentation

1 / 11

Unit 2 – Learning Goal 1. Inverse Functions. 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”

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

Inverse Functions

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

#### Presentation Transcript

Unit 2 – Learning Goal 1

## Inverse Functions

### 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

### 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

### Inverse Trig Functions

FunctionInverseSymbol

sinearcsinearcsin or sin-1

cosinearccosinearccosor cos-1

tangentarctangentarctanor tan-1

### 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

### Inverse Trig Functions

InverseFunction Defined from:

arcsinesin θ = y

arccosine cosθ =x

arctangenttan θ = y/x

### Inverse Trig Applications

Find the value for x.

24

x

26

### 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°

### 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

### 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”