4.1
AAT – Unit 4 Notes Packet
Graphs of Cosine, Sine and Tangent Functions
Name: _______________________________ Block: ______
Section
5-5
5-6
Topic
Graphing Sine and Cosine
Functions
Graphs of Other Trig Functions
Assignment
Practice #1, page 4.7
Practice #2, page 4.7
Practice #3, page 4.7
Quiz on Graphing Sine and
Cosine
Practice #4, page 4.12
Practice #5, page 4.12
Test Review, page 4.12
Test on Graphing Trig
Functions
Date Due:
4.2
Warm-up:
1. Go to: http:curvebank.calstatela.edu/unit/unit.htm
2. Watch how the unit circle is unwrapped to form the sine and cosine graphs.
3. Answer the questions on the website.
4. Definitions you will need to know:
Period:
Amplitude:
Odd Function:
Even Function:
Graphs of Sine and Cosine:
1. What is the maximum value?
2. What is the minimum value?
3. How long does the graph take to
go through one cycle?
4. Where does the graph cross the
x-axis?
5. What is the domain?
6. What is the range?
7. What patterns/symmetry do you notice about the graph of sine?
How to graph y  A sin( Bx)
Amplitude = A
2
B
i–M–i–m–i
Period =
4.3
Ex. 1 Graph y  3sin x
You Try: Graph the following:
1. y = -4sin(x)
Ex. 2 Graph y  2sin x
2. y = 0.5sin(x)
Ex 3: y = sin(2x)
You Try: Graph the following:
1 
3. y  sin  x 
2 
4. y  sin  3x 
4.4
Graph of cosine:
How is the graph of cosine similar to
the graph of sine? How is it
different?
x
Ex. 4: Graph y  4 cos  
3
You Try: Graph the following:
5. y  2cos  3x 
2
1 
6. y   cos  x 
3
5 
4.5
Pairs check with whiteboards - Graph
1. y  sin
1
x
2
3. y = 2cos3x
1
sin 2 x
2
1
4. y   cos
x
4
2. y  
Effects on Graph - A number added to x shifts the graph horizontally (Phase Shift).
To find Phase Shift: Set ___________ and solve.
Add (or subtract) that amount to x-values of
major points on table.


y = sin( x  ) shifts the graph
units left
4
4


Ex 1: Graph y  3cos  x  
6

You Try: Graph the following:


5. y  sin  x  
2


3
Ex2: Graph y  sin  x  
2
2


6. y  cos  x  
3

4.6
Pairs check with whiteboards - Graph
 
3
1. y  cos  x  
10 
5
1
sin  2 x   
2
 
 1
x
4. y   3sin 

8 
 4
2. y 


3. y   cos  3 x  
2

Summary so far of graphing sine and cosine:
y  A sin  Bx  C 
Feature of graph:
Period
What that is:
y  A cos  Bx  C 
How to find it:
Amplitude
Phase Shift
What happens when we add a number to the outside, e.g. y  sin x  1 ?
1
Ex: Graph: y   cos  6 x     3
2
4.7
Homework: For each practice set, graph on your own graph paper. State the amplitude, period, domain and
range. You may use your graphing calculator to verify your answers.
Practice #1
1. y = 3sinx
2. y = 2cosx
3. y = -2.5sinx
4. y = –cosx
5. y = sin3x
6. y = –cos2x
Practice #2
3
1. y  cos  x 
2
3
cos  x 
2. y 
2


3. y  sin  x  
2

3 
4. y  sin  x 
4 
3


5. y  cos  x  
2
3



6. y  2sin  x  
6

Practice #3
 

 1
2 

2. y   sin  3x  2   1
 
 1
x
3. y  2cos 
 1
2 
 2
 

4. y  sin  x 
2
4 

 

5. y  2cos  x 
2
6


 

6. y   3sin  x 
 1
3 

1. y  cos  2 x 
4.8
Graphs of Other Trig Functions
y  tan x
y  cot x
y  sec x
y  csc x
Graph of Tangent:
y  tan x
x
0

4

2
3
4
What does it mean for the graph when tangent is undefined?
Sketch the graph:

5
4
3
2
7
4
2
Graph of Cotangent:
y  cot x
x
0
Domain:
Range:
Period:
Range:
Period:
Sketch the graph:

4

2
3
4

5
4
3
2
7
4
2
Domain:
4.9
Ex 1: y  3cot x
You Try 1: y  2 tan x
1 
Ex 2: y  cot  x 
2 
3 
You Try 2: y  tan  x 
2 


Ex 3: y  tan  x  
2

You Try 3: y  cot  x  45
Pairs Check…
3


1. y  cot  x  
2
2


1
2. y  tan  x  
6
3

4.10
Graph of Secant: Use the graph of cosine
Graph of Cosecant: Use the graph of sine
1
Ex 1: y  sec x
2
You Try 1: y  2 csc x
4.11
1 
Ex 2: y  csc  x 
2 
You Try 2: y  sec  2x 


Ex 3: y  csc  x  
2



You Try 3: y  sec  x  
3

More Practice…
3


1. y  sec  x  
2
2


1
2. y  3csc  x  
4
2
4.12
Homework: For each practice set, graph on your
own graph paper. State the asymptotes, domain and
range. You may use your graphing calculator to
verify your answers.
.Practice #4
3
1. y  tan x
2


2. y  cot  x  
2

3 
3. y  tan  x 
4 
2 
4. y  cot  x 
3 

3
5. y  tan  x  
2
2
6. y  2cot  x   
Test Review
3
1. y  tan x .
2


2. y  cot  x   .
2

1 
3. y  csc  x  .
2 
4.
.


5. y  tan  x   .
2



6. y  cot  x   .
3

Practice #5
3
1. y  csc x
2
2. y   sec x


3. y  csc  x  
2

3 
4. y  sec  x 
4 

3
5. y  csc  x  
2
2
6. y  2sec  x   


7. y  sin  x   .
6



8.. y  cos  2 x   .
3

9.
.
10. y  3sin  2 x    .
11.
12.
13.
.
.
.