Unit 2 learning goal 1
Download
1 / 11

Inverse Functions - PowerPoint PPT Presentation


  • 179 Views
  • Uploaded on

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”

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

PowerPoint Slideshow about ' Inverse Functions' - lam


An Image/Link below is provided (as is) to download presentation

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

Unit 2 – Learning Goal 1

Inverse Functions


Transition 1 before and after
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
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
Inverse Trig Functions

Function Inverse Symbol

sine arcsine arcsin or sin-1

cosine arccosinearccosor cos-1

tangent arctangent arctanor tan-1


Inverse trig functions1
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 functions2
Inverse Trig Functions

Inverse Function Defined from:

arcsine sin θ = y

arccosine cosθ =x

arctangent tan θ = y/x


Inverse trig applications
Inverse Trig Applications

Find the value for x.

24

x

26


Solution
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
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
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”


ad