Math 114
Section 2.6 Graphs of Sine & Cosine Functions
Section 001
A. Basic Sine and Cosine Graph
Recall that both the sine and cosine functions are periodic; that is, every input value that is
2π radians apart, has the same output value.
When we begin to look at the graph of sine or cosine,
we only need to focus on [0,2π].
The rest of the graph will consist of repetitions of this portion of
the graph.
Graph of
.
sin
x
y
=
Properties of the Sine Function:
1. The domain is
).
,
(
∞
∞
2. The range is [1,1].
3. The sine function is odd (symmetric about the origin).
4.
The sine function has a period of 2π.
Graph of
.
cos
x
y
=
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Properties of the Cosine Function:
1. The domain is
).
,
(
∞
∞
2. The range is [1,1].
3. The cosine function is even (symmetric about the yaxis).
4.
The cosine function has a period of 2π.
B. Translations of the sine and cosine graphs.
B
x
A
y
+

=
)
sin(
ϕ
ϖ
B
x
A
y
+

=
)
cos(
ϕ
ϖ
A
tells us the amplitude, which is half the distance from the maximum value to the
minimum value.
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 Spring '08
 smith
 Math, Periodic function, Inverse function, Leonhard Euler, Cosine Graph Recall

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