Amplitude
Period
Translations

The graph of f(x)=sin x
Domain all Real numbers
Range -1 to 1

2
, 1


3

2
,

1




The graph of f(x)=sin x
Sin x is an odd function
3

2
, 1


2
, 1
 
2
,

1

3

2
,

1


Graph of f(x) = -sin x

Graph of the f(x) = Cos x
Domain: All real numbers
Range: -1 to 1

Graph of the f(x) = Cos x
Cos x is an even function


2

, 1
 
2

, 1


 
,

1
  
,

1


f ( x )
 cos( x )
 f ( x )
 sin

2 x
The red graph is Sin and the blue is Cos

Amplitude changes the Range

Amplitude changes the Range
Since Amplitude is a distance, it is always positive.
To find it: the absolute value of the Maximum minus the Minimum divide by two.
Amp is written before the function y = a*sin x

Amplitude changes the Range
Max 7; Min - 1 Amp. 7

(

1 )

4
2

2
, 7
 
,

1
2

Period (wave length)
The distance before the function repeats its value. y = sin bx; here b is 1.

Period (wave length) y = sin 2x b = 2
2

 period b

4
, 1

5

4
, 1


Translation to move the graph of the function y = sin (x + c): moves Right or Left
Here is y
 sin

2

Translation to move the graph of the function y = sin x + d moves up or down
Here is y
 sin x

2

With all the translations
The sine function is f(x) = d + a sin b(x +c)
The cosine function is f(x) = d + a cos b(x +c)

Applet for the Sine function
• http://www.analyzemath.com/trigonometry/ sine.htm

Homework
Page 307 – 310
#3, 9, 14, 20,
26, 32, 41, 49,
71, 78

Homework
Page 307 – 310
# 7, 12, 17, 23,
27, 36, 45, 60,
76, 86