April 29, 2016
Amplitude HW
1.
5
amplitude: 5
period: 2π
domain: (-∞,+∞ )
range: [-5, 5]
2.
amplitude: 3
period: 2π
domain: (-∞,+∞)
range: [-3, 3]
3.
4.
amplitude: 0.5
period: 2π
domain: (-∞ ,+∞ )
range: [-0.5, 0.5]
-5
0.5
-0.5
3
flip!
0.75
amplitude: -0.75
period: 2π
-0.75
domain: (-∞ ,+∞ )
range: [-0.75, 0.75]
0.83
5.
-3
amplitude: 0.83
flip!
period: 2π
domain: (-∞ ,+∞ )
range: [-0.83, 0.83]
-0.83
April 29, 2016
Homework Quiz
1. What is the domain of y = cosθ?
2. What is the range of y = cosθ ?
3. What is the maximum value of y = cos
θ?
4. What is the minimum value of y = cos
θ ?
5. What is the amplitude of the cosine function?
6. What are the x- and y- intercepts of the cosine function?
April 29, 2016
What change do you expect to see in the following functions, based on the
parent graph? Use your calculator to confirm your ideas.
y = sin x
y = sin 2x
( parent graph )
y = sin x
π
y = sin x
2
Now guess what the following graphs will look like when compared to the parent
graph.
( parent graph )
y = cos x
y = cos 3x
y = cos x
4
y = cos 2x
April 29, 2016
transformations
amplitude
period
....more to come!
April 29, 2016
Sine and Cosine are periodic functions. Periodic Functions are functions
that repeat themselves.
Period - horizontal length of one complete cycle.
April 29, 2016
The period for sin and cos is 2πor 360
|b|
State the period for each of the following functions:
a)
c)
b)
d)
o
|b|
But generally this
is NOT how I
recommend
graphing - pay
attention!
April 29, 2016
Graph
y = sin 3x
amplitude:
period:
Graph
y=cos
amplitude:
period:
April 29, 2016
A
C
E
G
B
D
F
H
April 29, 2016
y=-sinx
y=cosx y=sinx
y=3sinx y=-sin(2x)
y=2cos(3x)
y=2cosx
y=cos(3x)
April 29, 2016
More about the period of a sine graph....
April 29, 2016