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The Sine Function

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by

Maria Ramirez

on 1 October 2013

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Transcript of The Sine Function

f(x)=sin(x)
Parent Function
f(x)=sin(x)
Notes
Increasing/Decreasing Intervals
Boundedness
The
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.
Full transcript