1. Graphs of Sine and Cosine Sinusoids
Chapter 4, Section 4

2. Recall
How do the graphs of sine and cosine compare and contrast?

3. What is a sinusoid? if a function can be written in the form
where a, b, c, and d are constants and a, b are not 0, then the function is a sinusoid

4. Amplitude The amplitude of a sinusoid is
Graphically, the amplitude is ½ the height of the wave

5. Amplitude Examples

6. Period The period of a sinusoid is
Graphically, the period is the length of one full cycle of the wave

7. Period Examples

8. Frequency The frequency of a sinusoid is
Graphically, the frequency is the number of complete cycles the wave completes in a given interval.

9. Frequency Examples

10. Phase Shift
The phase shift of a sinusoid is

11. Phase Shift Examples

12. Determine the following:
Amplitude
Period
Vertical stretch or shrink
Horizontal stretch or shrink
Phase shift
Frequency
Vertical translation

13. Homework page 394 #5,10, 15, 45, 50, 55, 61-68 odd Exit Slip:
If the amplitude is ½ the height of the wave, what type of transformation is this?
If the period is the length of one full cycle of the wave, what type of transformation is this?
What type of transformation is the phase shift?