Comparing Bike Pedal Motion to Sine Function Graph
Think about riding a bike and pumping the
pedals at a constant rate of one revolution each
second.
How does the graph of the height of one of your
feet compare with the graph of a sine function?
13-7
Translating Trigonometric Functions
Today’s Objective:
I can write and graph a trigonometric
functions.
Translating Functions
Horizontal
Vertical
Phase Shift
Translate
h
units horizontally
Translate
k
units vertically
Midline:
y
=
k
h
Family of Trigonometric Functions
Parent Functions
Transformed Function
Amplitude: Vertical stretch or shrink
Period
Phase shift: Horizontal shift
Vertical shift :
y
=
k
is midline
Graph each function on interval from 0 to 2
π
Amplitude:
Graphing:
1.
Sketch in Midline (
y
=
k
)
2.
Graph beginning point
with phase shift.
3.
Graph remaining four
points.
Phase Shift:
Midline:
Period:
Graph each function on interval from 0 to 2
π
Amplitude:
Graphing:
1.
Sketch in Midline (
y
=
k
)
2.
Graph beginning point
with phase shift.
3.
Graph remaining four
points.
Phase Shift:
Midline:
Period:
Write a sine and cosine function for the graph.
p. 880: 22-25, 27, 28, 31, 33, 44, 45
Ch. Test Review p. 897: 1, 3-14, 17-20, 25-30, 32
W.S. Translating Sine and Cosine Functions
Graph each function on interval from 0 to 2
π
Amplitude:
Graphing:
1.
Sketch in Midline (
y
=
k
)
2.
Graph beginning point
with phase shift.
3.
Graph remaining four
points.
Phase Shift:
Midline:
Period:
When riding a bike and pumping the pedals at a constant rate, the graph of the height of one foot follows a pattern similar to a sine function. Understanding the relationship between the two graphs can help in visualizing trigonometric functions and their translations.
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Presentation Transcript
Think about riding a bike and pumping the pedals at a constant rate of one revolution each second. How does the graph of the height of one of your feet compare with the graph of a sine function?
13-7 Translating Trigonometric Functions Today s Objective: I can write and graph a trigonometric functions.
Translating Functions Vertical ?(?) Horizontal ?(?) Translate h units horizontally ? ? + ? ?(? ) Translate k units vertically Midline: y = k Phase Shift ? = ??? ? ? ? = ??? ? + ? ? h=? ? ? = ? ? = ???(?) ? = ???(?)
Family of Trigonometric Functions Parent Functions Transformed Function ? = ? sin?(? ?) + ? ? = ? cos?(? ?) + ? ? = sin? ? = cos? ? = Amplitude: Vertical stretch or shrink 2? ? =Phase shift: Horizontal shift = Period ? =Vertical shift : y = k is midline
Graph each function on interval from 0 to 2 ? = sin ? +? 2 Amplitude: Midline: 1 2 ? = 2 Period: 2? Left ? Phase Shift: 2 Graphing: 1. Sketch in Midline (y = k) 2. Graph beginning point with phase shift. 3. Graph remaining four points.
Graph each function on interval from 0 to 2 ? = 2cos ? ? 3 Amplitude: Midline: 2 + 1 ? = 1 Period: 2? Right ? Phase Shift: 3 Graphing: 1. Sketch in Midline (y = k) 2. Graph beginning point with phase shift. 3. Graph remaining four points.
Write a sine and cosine function for the graph. ? = ? sin?(? ?) + ? ? ? ? = sin (? ) + ? ? ? ? = ? cos?(? ?) + ? ?? ? ? = cos (? ? ) + ? ?
Graph each function on interval from 0 to 2 ? = 3sin2 ? ? 6 Amplitude: Midline: 3 + 2 ? = 2 Period: ? Right ? Phase Shift: 6 Graphing: 1. Sketch in Midline (y = k) 2. Graph beginning point with phase shift. 3. Graph remaining four points.
