Use the information on page 822 to explain how you can predict the behavior of tides. Explain why c

Use the information on

page 822

to explain how you can predict the behavior of tides. Explain why certain tidal characteristics follow the patterns seen in the graph of the sine function.

14-1
Graphing Trigonometric
Functions
Hiche ,
Pulloc
Main Ideas
Graph trigonometric
functions
. Find the amplitude
and period of
variation of the sine,
cosine, and tangent
functions
New Vocabulary
amplitude
GET READY for the Lesson
The rise and fall of tides can have
great impact on the communities
and ecosystems that depend
upon them. One type of tide is a
semidiurnal tide. This means that
bodies of water, like the Atlantic
Ocean, have two high tides and
two low tides a day. Because
tides are periodic, they behave
the same way each day.
Tdal
Rapi
Sul We
Lel
Low Tide
Graph Trigonometric Functions The diagram below illustrates the water
level as a function of time for a body of water with semidiurnal tides.
High The
Water
Level
10
14
120 22
24 Tme
Review
Vocabulary
Period the least
possible value of a for
which f(x) – Rx+ a)
In each cycle of high and low tides, the pattern repeats itself. Recall that
a function whose graph repeats a basic pattern is said to be periodic.
To find the period, start from any point on the graph and proceed to the
right until the pattern begins to repeat. The simplest approach is to begin
at the origin. Notice that after about 12 hours the graph begins to repeat.
Thus, the period of the function is about 12 hours.
“To graph the functions y = sin , y = cos Bor y = tan 8, use values of
expressed either in degrees or radians. Ordered pairs for points on these
graphs are of the form (, sin 8), (0,cos 8), and (@tan 8), respectively.
30
120
135
100
20
200 201
S1
360
es
45
V
7
Vs
1
}
0
nearest
0
0.5
0.7
0.9
09
05
-05
-02
-05
0
CS
1
vi
va
1
1
T–
De
1
0.9
0.7
0.5
D
.
S-SHOT
– Hale
1
09
0.7
as
0.5
– 2 2 – – –
1
–
ISHT
tano
0
VI
1
VS
-VS
-1
vs
.
Vs
-V
–
—
nearesi
tenth
0
06
1
17
-17
-1
.
06
1
-U
-06
0
*
4
1
1
1
21
nd not defined
822 Chapter 14 Trigonometric Graphs and Identities