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Inverse Functions

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Unit 2 – Learning Goal 1

Inverse Functions

- 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

- 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

FunctionInverseSymbol

sinearcsinearcsin or sin-1

cosinearccosinearccosor cos-1

tangentarctangentarctanor tan-1

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

InverseFunction Defined from:

arcsinesin θ = y

arccosine cosθ =x

arctangenttan θ = y/x

Find the value for x.

24

x

26

- 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°

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

- 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”