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Transcript
6.3

6.3
Graphing Sine and Cosine
Functions
Periodic Functions
• A periodic function is a function with a
repeating pattern this includes sin and
cos graphs.
• How long does it take for the graph to
repeated itself?
360 ( for degrees) OR
2 (for radians)
Periodic Functions
• A periodic function f exists if there is a
positive constant p so:
f (s+p ) = f (s)
P is the period (provided it is the least
possible value)
y
1.0
0.8
0.6
0.4
0.2
-6
-5
-4
-3
-2
-1
1
-0.2
-0.4
-0.6
-0.8
-1.0
y = sinx
2
3
4
5
6
x
Characteristics of the Sine Function
1. The domain is the set of all real numbers.
2. The range consists of all real numbers
from -1 to 1, inclusive.
3. The sine function is an odd function
(symmetric with respect to the origin).
4.
Characteristics of the Sine Function
5.
6.
Ex.
• Find the value of 9pi/2 by using the graph
of the sine function.
• Find the values of theta for which
– sin(theta) = 0 is true
Graph y = sin(x) from 3pi to 5pi
1.5
(0, 1)
0
1.5
2
4
6
Characteristics of the Cosine Function
1. The domain is the set of all real numbers.
2. The range consists of all real numbers
from -1 to 1, inclusive.
3. The cosine function is an even function
(symmetric with respect to the y-axis).
4.
5.
Characteristics of the Cosine Function
6.
The graphs of the sine and cosine
functions are called sinusoidal
graphs.
Ex:
• #33 on p.364
• Graph y = cos(x) from -5pi to -3pi inclusive