Transcript 6.4 – Amplitude and Period of Sine and Cosine Functions

6.4 – Amplitude and Period of Sine
and Cosine Functions
Let’s review
 How would the graph of g(x) = 3x2 compare to the parent
graph of f(x) = x2
Amplitude
 The similar effect will happen for sine and cosine
functions. Not only to 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
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
y = -2cosθ
State the amplitude
b) Graph the function and y = cosθ on the same set of axes.
c) Compare the graphs.
a)
In your calculator, graph the following
functions in the same window
y = sinθ
2. y = sin(4θ)
3. y = sin(θ/4)
1.
Compare the three graphs
Period
 The period of the functions y = sin(kθ) and y = cos(kθ)
is 2π/k, where k > 0
State the period of the functions.
1.
y = cos(θ/3)
2.
y = sin(6θ)
Write an equation of the cos function
given the amplitude and period
1.
amplitude: 17.9; period: π/7
2.
Amplitude: 5/3; period: 30