Parent Function

f(x)=sin(x)

Notes

Increasing/Decreasing Intervals

Boundedness

**The**

Sophisticated

Sine

Function

!

B

Double

M

Double

U

Sophisticated

Sine

Function

!

B

Double

M

Double

U

Introduction

Today you will learn the following:

The Parent Function of the Sine Function

The Sine Parent Function Graph

Domain of the Sine Function

Range of the Sine Function

Whether the Sine Function is continuous, or it has discontinuity

Whether the Sine Function is Bounded or Unbounded

Local Extrema of the Sine Function (Maximum, Minimum)

Symmetry of the Sine Function

Asymptotes of the Sine Function

End Behavior of the Sine Function

Interesting Facts about the Sine Function

Who discovered the Sine Function

When the Sine Function was discovered

Real Word Applications of the Sine Function

DOMAIN AND RANGE

Who

discovered

the

Sine

Function

and

when

was

it

discovered

?

-Aryabhata

(476-550)A.D.

-500 A.D.

X Y

-2 -.9093

-1 -.84150

0 0

1 .84147

2 .9093

Interval Notation:

Domain:(-infinity∞, +infinity∞)

Range: (-1,1)

The Sine Function is bounded above and below.

Local Extrema

Max.

:

(pi/2,1)

Min.

: (3pi/2 ,-1)

X-Intercepts:

(pi,0),(2pi,0)

Symmetry

ODD!

Interesting Fact!

Take a closer look!

Does the Sine Function have asymptotes?!?...

Asymptotes

The Sine Function is Continuous!

Repeating increasing and decreasing intervals.

From 0 to 2pi, sin X is increasing on the intervals

on the intervals (0,pi/2) and (3pi/2, 2pi), and decreasing on the interval (pi/2, 3pi/2)

End Behavior

Real World Applications!

It will keep on going forever!

y=1

y=-1

c1

NO, the Sine Function has no asymptotes!

It doesn't have end behavior, because it oscillates from 1 to -1!

http://animoto.com/play/TSpYIfv18M0x01robNKzIw

Periodical and Cyclical Behavior

Employment over a period of time!

Temperature over a period of time!

http://animoto.com/play/JCGjSPgDNNkjZwsUkh6mRw

Y

o

u

a

r

e

done!

Pop Quiz

What is the Parent Function of the Sine Function!?

The Sine Function starts at zero!

Where does the Sine Function start?

What is the Domain and Range of the Parent Sine Function?

What type of Symmetry does the Sine Function have?

Is the Sine Function Continuous?

Is the Sine Function Bounded?

Does the Sine Function have Asymptotes?

Who Discovered the Sine Function?

Give one real world application of the Sine Function?

The Sine Function is everywhere!

The Sine Function and the Sinus Cavities in your head derive their names form a common root: the Latin word for "bay." This is is due to a 12th century mistake made by Robert of Chester who translated a word incorrectly from and Arabic manuscrpt.