1. 6.4 – Amplitude and Period of Sine and Cosine Functions

2. Let’s review
How would the graph of g(x) = 3x2 compare to the parent graph of f(x) = x2

3. Amplitude
The similar effect will happen for sine and cosine functions. Not only do they stretch the graphs, it changes the maximum values.
The maximum value of y = Asinθ or y = Acosθ is equal to |A|
The absolute value of A is called the amplitude

4. Amplitude
It can also be described as the absolute value of half the difference of the maximum and minimum values of the function.
Example: y = 4sinθ
The amplitude is 4…
The maximum is 4 and the minimum is -4. So (4 - -4)/2 = 4

5. y = -2cosθ State the amplitude
Graph the function and y = cosθ on the same set of axes.
Compare the graphs.

6. Period
The period of the functions y = sin(kθ) and y = cos(kθ) is 2π/k, where k > 0

7. State the period of the functions.
y = cos(θ/4)
y = sin(6θ)
State the amplitude and period of the function
y = 5 cos 2x
1. 6pi pi/3

8. Write an equation of the cos function given the amplitude and period
amplitude: 17.9; period: π/7
Amplitude: 5/3; period: 30