1. Translations of Sine and Cosine Functions
Ch.6 Section 5
Translations of Sine and Cosine Functions

2. A phase shift is simply a horizontal change.
The phase shift of the function y = A cosk( + C) is C. If C > 0, the shift is to the left. If C < 0, the shift is to the right.

3. Example
State the phase shift of the following function. Then sketch the function and y = cos on the same coordinate plane.

4. Fine the phase shift of…

5. A vertical shift is simply a vertical change.
The vertical shift of the function y = Asink + C is C. If C > 0, the shift is up. If C < 0, the shift is down.

6. Example
State the vertical shift of the following function. Then sketch the function and y = cos on the same coordinate plane.

7. State the amplitude, period, phase shift, and vertical shift for

8. Write an equation of a sine function with amplitude of 4, period π, phase shift –π/8, vertical shift 6.
1, 2, 3 go!

9. Graphing Compound Functions
You need to make a table of values to find the pattern.
Graph y = x + cos(x)