Download Lesson 2 - Coweta County Schools

Notes Over 14.2
Translations of Trigonometric Graphs
Translation of a Sine Function
y  sin x 1
1
1
1

2

3
2
2
Amplitude 1
Period
2
Notes Over 14.2
Translations of Trigonometric Graphs
Translation of a Sine Function
1
1

2

3
2
2


y  sin  x 
 
2

Amplitude 1
Period
2
Notes Over 14.2
Graphing a Vertical Translation
Graph the function.
1. y  2  cos x
1
Amplitude
Translation
down 2
Period
2

1
3
2

3
2
2
Notes Over 14.2
Graphing a Vertical Translation
Graph the function.
2. y  3  sin x
4
1
Amplitude
Translation
up 3
Period
2
2

2

3
2
2
Notes Over 14.2
Graphing a Vertical Translation
Graph the function.
3. y  3  tan x

Translation
down 3
Period



2

2
2
4

Notes Over 14.2
Graphing a Horizontal Translation
Graph the function.
4. y  sin  x   
Amplitude
Period
1
2
Translation
right 
1
1

2

3
2
2
Notes Over 14.2
Graphing a Horizontal Translation
Graph the function.
5. y  cos  x   
Amplitude
Period
1
2
Translation
left 
1
1

2

3
2
2
Notes Over 14.2
Graphing a Horizontal Translation
Graph the function.


6. y  3 cos x  
2

Amplitude
Period
3
2
Translation
right /2
3

2
3

3
2
2
Notes Over 14.2
Graphing a Reflection
Graph the function.
7. y   cos x
Amplitude
Period
1
2
Reflection
over x-axis
1

1
2

3
2
2
Notes Over 14.2
Graphing a Reflection
Graph the function.
1
7. y   sin x
2
1
Amplitude
2
Period
1
2
Reflection
over x-axis

2
1

3
2
2
Notes Over 14.2
Graphing a Reflection
Graph the function.
1
8. y  3 tan x
2
Period
2

1/ 2
Reflection
over x-axis
3
 2
3


2
Notes Over 14.2