Trigonometric Functions and Graphs, algebra homework help

Please complete the following questions. It is important that you show all work you did to solve the problems when you submit your work. This includes any calculations, diagrams, or graphs that helped you solve it.

1. OPEN ENDED Write an equation giving the value of the Cosine function for an angle measure in its domain. Then, write your equation in the form of an inverse function.
2. OPEN ENDED Write the equation of a trigonometric function with a phase shift of -45°. Then graph the function, and its parent graph.
3. Writing in Math If the formula for the temperature T in degrees Fahrenheit of a city t months into the year is given by T = 50 + 25 sin(6t), explain how to find the average temperature and the maximum and minimum predicted over the year.
4. Writing in Math Use the information on page 842 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
GET READY for the Lesson
Main Ideas
• Graph trigonometric
functions.
High Tide
Period
Tidal
Range
• Find the amplitude
and period of
variation of the sine,
cosine, and tangent
functions.
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.
Still Water
Level
Low Tide
New Vocabulary
amplitude
Graph Trigonometric Functions The diagram below illustrates the water
level as a function of time for a body of water with semidiurnal tides.
High Tide
Water
Level
++ ++ +
4 6
8 10 12
+
18 20 22
–
2
14
16
124 Time
-Low Tide
Review
Vocabulary
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.
Period The least
possible value of a for
which f(x) = f(x + a).
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 0, y = cos 0, or y = tan 0, use values of
expressed either in degrees or radians. Ordered pairs for points on these
graphs are of the form (0, sin 0), (0, cos ), and (@, tan 8), respectively.
1
00
30°
45°
60°
90°
120°
135°
150°
180°
210°
225°
240°
270°
300°
315°
330°
360°
sin e
1
1
V2
0
17
VS
을
1
3
2
1
V3
2
V2
2
2
플
0
v3
-1
V2
글
0
2
2
2
2
2
2
nearest
tenth
0
0.5
0.7
0.9
1
0.9
0.7
0.5
0
-0.5
-0.7
-0.9
-1
-0.9
-0.7
-0.5
0
.
cos e
V2
1
1
V3
2
1
V2
1
0
V3
V3
-1
V2
2
0
2
-IN
2
V2
2
1
V3
2
.
2
2
2
2
nearest
tenth
1
0.9
0.7
0.5
0
-0.5
-0.7
-0.9
-1
-0.9
-0.7
-0.5
0
0.5
0.7
0.9
1
.
tane
0
V3
1
V3
nd
– V3
-1
V3
0
V3
3
V3
1
VS
nd
– V3
-1
0
.
3
3
3
nearest
tenth
0
0.6
1
1.7
nd
-1.7
-1
-0.6
0
0.6
1
1.7
nd
-1.7
-1
-0.6
0
T
T
기
T
e
0
27
3
ST
4
T
7
6
5
ST
4
47
3
ST
2
뜰
5 0
3
IT
Im
6
2 0
3
6
4
픈 풍
쪽 51
nd = not defined
822 Chapter 14 Trigonometric Graphs and Identities