Trigonometry Section 4.1
Graph each defined function over the interval
 2 ,2 .
Give the amplitude.
2
sin x
3
1.
y  2 cos x
2.
y  3 sin x
3.
y
4.
y
3
cos x
4
5.
y   cos x
6.
y   sin x
7.
y  2 sin x
8.
y  3 cos x
Graph each defined function over a two-period interval. Give the period and the amplitude.
9.
y  sin
2
x
3
10.
3
y   cos x
4
11.
y   sin 3x
12.
y  cos 2 x
13.
y  2 sin
1
x
4
14.
y  5 cos 3x
15.
y  cos x
16.
y   sin  x
17.
y
1
1
cos x
2
2
Match each defined function with its graph.
18.
y  sin x
19.
y  cos x
20.
y   sin x
21.
y   cos x
22.
y  sin 2 x
23.
y  cos 2 x
24.
y  2 sin x
25.
y  2 cos x
Trigonometry Section 4.2
Match each function with its graph.
1.


y  sin  x  
4

2.


y  sin  x  
4

3.


y  cos x  
4

4.


y  cos x  
4

5.
y  1  sin x
6.
y  1  sin x
7.
y  1  cos x
8.
y  1  cos x
Find the amplitude, the period, any vertical translation, and any phase shift of each graph.
2 

sin  x  
3 
2
9.
y
11.


y  3 cos 2 x  
4

10.
2

y   cos  x  
3
3
12.
y  1 
1
cos2 x  3 
2
Graph the defined function over a one-period interval.


y  sin  x  
3

3 

y  3 sin  x 

2 

13.


y  cos x  
2

16.
2
x 
y   cos   
3
2 4
17.
1


y   cos 4 x  
2
2

18.
y  3 cos4 x   
19.
1 3

y   sin  x  
4 4
8
14.
15.
Graph the defined function over a one-period interval.
20.
y  2  3 cos x
22.
y 1
2
1
cos x
3
2
1
sin 3x
2
21.
y  2 
23.
y  3  3 sin
1
x
2
Graph the defined function over a one-period interval.
24.


y  3  2 sin  x  
2

26.


y  1  cos  2 x  
2

25.
5


y    cos 3  x  
2
6

Trigonometry Section 4.3
Match each equation with its graph.
1.
y   csc x
2.
y   sec x
3.
y   tan x
4.
y   cot x
5.


y  tan  x  
4

6.


y  cot  x  
4

9.

1
y   sec  x  
3
2
Graph each defined function over a one-period interval.
7.


y  csc  x  
4

10.

1
y  csc x  
4
2
12.
y 2
8.
1
1

sec  x   
4
2

3 

y  sec  x 

4 

11.


y  1  2 csc  x  
2

13.
1
x  
y  sec 
 
3
 2 2
Graph each defined function over a one-period interval.
14.
y  2 tan x
15.
y
1
cot x
2
1
x
4
16.
y  2 tan
19.
y  2  tan x
22.
y  1  2 cot x
Graph each defined function over a one-period interval.
17.
y  tan 2 x   
18.


y  cot  3x  
4

20.
y  1  cot x
21.
y  3
23.
y  1 
25.
x  
y  0.1tan 
 
 4 4
1
cot 2 x  3 
2
1
tan x
2
24.
y  2  3 tan 4 x   
TRIGONOMETRY
NAME: _________________________
Practice Test: GRAPHS OF THE CIRCULAR FUNCTIONS
Match each function with its graph.
1.
y  3cos x
2.
y  sin 3x
3.
y  3  cot x
4.
y   tan x
5.
1
y  sec x
3
6.


y  csc  x  
3

7.
y  3  sin x
8.


y  cot  x  
3

9.
1
y  tan x
3
Find the amplitude, the period, the reflection, any vertical translation, and any phase shift of each
graph.
10.
1
y   cos 3x
2
11.
1
y  2  sin 3x
2
12.


y  csc  x  
4

13.
1
1

y  2  sec  x   
4
2

14.


y  3tan 4  x  
4

15.
1
y  1  cot  2 x  3 
2
Graph each defined function over a one-period interval.
16.
y
19.
22.
1
sec x
2
17.
y  1  csc x
18.
y  tan 3x
 x 3 
y  cot  

2 4 
20.
y  1  3sin 2 x
21.
1
y  1  cos  2 x   
2
y  2 cos x
23.
y
1
cot 3x
2
24.
y  1  csc  2 x   
Matching graphs for Questions 1 – 9
SOLUTIONS
1.
F
2.
B
3.
E
4.
C
5.
A
6.
H
7.
I
8.
D
9.
G
10.
Amplitude =
1
2
, Period =
, Reflection, Vertical Trans. = none, Phase Shift = none
2
3
11.
Amplitude =
1
2
, Period =
,No Reflection, Vertical Trans. = 2 down,
2
3
Phase Shift = none
12.
Amplitude = 1 , Period =
Phase Shift =
4
, No Reflection, Vertical Trans. = none,
left
1
, Period = 4 ,No Reflection, Vertical Trans. = 2 up,
4
Phase Shift = 2 right
13.
Amplitude =
14.
Amplitude =
3 , Period =
Phase Shift =
15.

2

4

, No Reflection, Vertical Trans. = none,
4
left
1

, Period =
, No Reflection, Vertical Trans. = 1 down,
2
2
3
right
Phase Shift =
2
Amplitude =
TABLE ANSWERS OR ORDERED PAIR ANSWERS are available if you want to see the
ordered pairs and work for the practice test