1. How do we recognize and graph periodic and trigonometric functions?
Graphs of Sine and Cosine
Essential Questions
How do we recognize and graph periodic and trigonometric functions?
Holt McDougal Algebra 2
Holt Algebra 2

2. Translations of Trigonometric Graphs
Translation of a Sine Function
Amplitude
Period

3. Translations of Trigonometric Graphs
Translation of a Sine Function
Amplitude
Period
Moving a graph left or right is called a phase shift.

4. You can combine the transformations of trigonometric functions
You can combine the transformations of trigonometric functions. Use the values of a, b, h, and k to identify the important features of a sine or cosine function.
Amplitude
Phase shift
y = asinb(x – h) + k
Vertical shift
Period

5. Translations of Trigonometric Graphs
Draw one cycle of the function’s graph.
Amplitude
Period
Translation
down 2

6. Translations of Trigonometric Graphs
Draw one cycle of the function’s graph.
Amplitude
Period
Translation
up 3

7. Translations of Trigonometric Graphs
Draw one cycle of the function’s graph.
Amplitude
Period
Translation
right p

8. Translations of Trigonometric Graphs
Draw one cycle of the function’s graph.
Amplitude
Period
Translation
left p

9. Translations of Trigonometric Graphs
Draw one cycle of the function’s graph.
Amplitude
Period
Translation
right p/2

10. Translations of Trigonometric Graphs
Draw one cycle of the function’s graph.
Amplitude
Period
Reflection over x-axis

11. Translations of Trigonometric Graphs
Draw one cycle of the function’s graph.
Amplitude
Period
Reflection over x-axis

12. Lesson 11.1 Practice B