Section 5.2 – Graphs of the Sine and Cosine Functions
1
Section 5.2
Graphs of the Sine and Cosine Functions
A Periodic Function and Its Period
A nonconstant function
f
is said to be
periodic
if there is a number
p
> 0 such that
f
(
x + p
) =
f
(
x
) for all
x
in the domain of
f
.
The smallest such number
p
is called the period
of
f
.
The graphs of periodic functions display patterns that repeat themselves at regular intervals.
Amplitude
Let
f
be a periodic function and let
m
and M denote, respectively, the minimum and
maximum values of the function.
Then the
amplitude
of
f
is the number
2
m
M

.
In other words the amplitude is half the height.
Example 1:
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Section 5.2 – Graphs of the Sine and Cosine Functions
2
Now let’s talk about the graphs of the sine and cosine functions.
Recall:
sin(
2
)
sin
θ
π
θ
=
and
cos(
2
)
cos
θ
π
θ
=
This means that after going around the unit circle once (
2
π
radians), both functions
repeat.
So the period of both sine and cosine is
2
π
.
Hence, we can find the whole
number line wrapped around the unit circle.
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 Fall '08
 Staff
 Trigonometry, Periodic function, cosine functions

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