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Chapter 7 Review
Complete the chart then graph each function on the provided graphs. If it does not apply
or there is not one, state so. [1 pt each box, total 24 pts]
Function
Amplitude
Period
Phase Shift
Vertical Shift
1
 x    1
2
y  3cos  2x     4
y  2 tan
1
y   sin 2 x  3
2
y  csc  x     2


y   sec 2  x  
2

y  2cot  x     3
Graph each of the above functions. Make sure you graph ONE complete cycle to the left
and to the right after you shifted the origin. [5 pts each, total 30 pts]
1) y  2 tan
1
 x    1
2
4) y  csc  x     2
2) y  3cos  2x     4


5) y   sec 2  x  
2

1
3) y   sin 2 x  3
2
6) y  2cot  x     3
Multiple Choice: Write the answer for the following problems on the line provided. [4
pts each, total 24 pts]
_____ 7) The period for y  4sin  ( x  1)  1 is:
A) 1
B) 
C) 4
D) 2
_____ 8) Which trigonometric function listed is EVEN?
A) sine
B) cosecant C) tangent
D) cosine
E) None of these
E) None of these
_____ 9) What is the domain for y  9cos 2  x     1
A)
 ,  
B)  1,1
C)  8,10
_____10) Where are the asymptotes for y  tan x ?
A) k where k is any integer.
B) k where k is any ODD integer.
k
C)
where k is any integer.
2
k
D)
where k is any ODD integer.
2
E) None of these.
_____11) Where are the asymptotes for y  csc x
A) k where k is any integer.
B) k where k is any ODD integer.
k
C)
where k is any integer.
2
k
D)
where k is any ODD integer.
2
E) None of these.
_____12) Given the graph to the right, determine
which equation it best resembles.
A) y = 4 sin 2x + 1
B) y = 3 sin 4x
C) y = 3 sin 2x + 1
D) y = 3 sin 2x – 1
E) y = 2 sin 4x + 1
D)  2 , 2  E) None of these
Modified True/False. Determine if the state is true or false. IF it is false, correct the
underlined word. [2 pts each for T/F and 2 pts to correct the false].
True False _______________ 13) Period is defined by the number of times you see a
complete cycle from 0 to 2.
True False _______________ 14) Sine and Cosecant are the only 2 trigonometric
functions that when graphed do not have asymptotes.
True False _______________ 15) Tangent does not have an amplitude since it has a
range of  ,   .
Write the equation the periodic function with the following changes [4 pts each]:
16) y = sin x with an Amplitude of ¼ , period of , phase shift of right

and vertical
4
shift of up 2 .
17) y = tan x with a reflection across the x-axis, period of 4, phase shift of
2
, and
3
vertical shift of down 1.
18) Explain how knowing the unit circle helps you graph y = sin x and y = cos x. You
must explain this in AT LEAST 3 sentences.
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19. Find all solutions from 0 to 2.
(hint: You may want to use the unit circle to help you find all of them.)
1
sin   1   .
2