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Trigonometry 1.2:
Translations in Periodic Functions
Student Name:
Practice Problems
Graph the following pairs of trigonometric functions. For each pair of functions, describe the change that you see. The first function is graphed in blue, the second function is graphed in red.
The first problem has been graphed for you. To continue, copy the input command, change the function to your problem, and press 
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1. Sin[x] 2+Sin[x]
Change Observed:
2. Cos[x] 1+Cos[x]
Change Observed:
3. Sin[x] -1+Sin[x]
Change Observed:
4. Cos[x] -2+Cos[x]
Change Observed:
5. Sin[x] Sin[x-1]
Change Observed:
6. Sin[x] Sin[x+2]
Change Observed:
7. Cos[x] Cos[x-1]
Change Observed:
8. Cos[x] Cos[x+2]
Change Observed:
9. Sin[x] 2+Sin[x-2]
Change Observed:
10. Sin[x] 2+Sin[x+2]
Change Observed:
Now Look at the Definitions!
Phase Shift
The phase shift is a movement, or shift, of the entire function horizontally (along the x-axis).
Average y-Value
The average y-value is a movement, or shift, of the entire function vertically (along the y-axis).
    
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