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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”

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Inverse Functions

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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

FunctionInverseSymbol

sinearcsinearcsin or sin-1

cosinearccosinearccosor cos-1

tangentarctangentarctanor 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

InverseFunction Defined from:

arcsinesin θ = y

arccosine cosθ =x

arctangenttan 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


Evaluating inverse functions

Evaluating Inverse Functions


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”


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