Download test-3-a-solutions

Circle your answer choice on the exam AND fill in the answer sheet below with the letter of the
answer that you believe is the correct answer.
Problem
Number
Letter of Answer
Problem
Number
Letter of Answer
Problem
Number
Letter of Answer
2.
B
8.
D
14.
B
3.
A
9.
D
15.
B
4.
C
10.
D
16.
C
5.
D
11.
C
17.
C
6.
D
12.
B
18.
E
7.
B
13.
B
19.
A
For Part I – Free Response. Show all work (as described on page 1).
1. [10 pts] Verify the following trigonometric identity
cos(t )  cos 3 (t )
 cos(t ) sin( t )
sin( t )
MAT 170 Test 3 Form A Solutions (Fall 2011)
For Part II – Multiple Choice: Circle your answer choice on the exam AND fill in the answer
sheet on the front of page 2 with the letter of the answer that you believe is the correct answer.
2. [5 pts]
The equation of the graph below can be written as f ( x)  A cos( Bx ) . What is
period for this graph?
A. 3
3. [5 pts]
B. 4
C.
Given that cos( )  
A. 
5. [5 pts]
C.

2
D.

4
E. None of these
The equation of the graph given in problem 2 can be written as f ( x)  A cos( Bx ) .
What is A for this equation?
A. 3
4. [5 pts]
B. 4
77
2
B.

2
9
8
B.
E. None of these
2
and tan( )  0 , find the exact value of sin(  ) .
9
77
9
7
8
MAT 170 Test 3 Form A Solutions (Fall 2011)
77
9
C. 
Find the reference angle for 
A.
D. 6
D.  77
E. None of these
7
.
8
C. 

8
D.

8
E. None of these
6.
   5
[5 pts] Find the exact value for the expression sin 1  sin 
  6
A.
7.
 5
6
B.
 4
6
B. 100765.4 feet
D. 11358.9 feet
 
 3
[5 pts] Evaluate sin   cos    2 tan 
3
 4
2 3
2
2 3
C.
2
A.
9.
 2
6
D.

6
E.

6
[5 pts] A plane is flying at an elevation of 27000 feet. It is within sight of the airport and
the pilot finds that the angle of depression to the airport is 15°. Find the distance
between a point on the ground directly below the plane and the airport. Round
your answer to the nearest tenth of a foot.
A. 104320.0 feet
C. 7234.6 feet
8.
C.

  .

[5 pts] If cos( ) 
A. 0
10. [5 pts]
E. None of these

.

B. Answer is undefined.
D.
4 3
2
E. None of these
5
and  is in quadrant IV, then the value of tan(  ) csc( ) is
9
9
5
B.
C. 1
D.
E. None of these
9
5
4
If tan( )   , in what quadrant(s) may  be located?
3
4
A. It is not possible for tan( )   .
3
B. Quadrant II only
C. Quadrants I and III
D. Quadrants II and IV
E. None of these
MAT 170 Test 3 Form A Solutions (Fall 2011)

 x 
11. [5 pts] Rewrite the expression tan  sin 1    as an algebraic expression in x
 6 

A.
x
6 x
x
C.
6
B.
D.
36  x 2
36  x 2
x
6
E. None of these


12. [5 pts] Given that f ( x)  8 sec 2 x   , what is the range of f(x).
7

A.  8, 8
C.  8, 8
B.  ,  8  8, 
D.  , 
E. None of these


13. [5 pts] Given f ( x)  10 cos10 x   , find the phase shift.
8



B. left
80
80
E. None of the above
A. right
C. right

8
D. left

8


14. [5 pts] Given f ( x)  4 cos 7 x   , find the period.
9

A.

9
B.
2
7
C. 7
D. 2
E. None of the above
15. [5 pts] What is the range of the tangent function?
A.
(1, 1)
B.
(, ) C. [1, 1]
D. [0, )
E. None of the above


16. [5 pts] Given f ( x)  10 sin 10 x   , find the amplitude.
8

A. 5
B. –5
MAT 170 Test 3 Form A Solutions (Fall 2011)
C. 10
D. –10
E. None of the above
17. [5 pts]
    2 
    2 
Find the exact value of cos  cos
  sin   sin 

 12   3 
 12   3 
A. 
1
2
B.
2
2
C. 
2
2
D. 
3
2
E. None of the above
18. [5 pts] Which of the following choices is the same (in value) as sin( 60  45) ?
A. sin 60  sin 45
B. sin( 345)
C. sin 60 cos 45  cos 60 sin 45
D. A, B, and C all have the same value as the original
E. B and C have the same value as the original
F. A and C have the same value as the original
19. [5 pts] Convert 7.5 radians to degrees.
A.
1350

degrees
B.
7.5
degrees C. 1350 degrees
180
D. the angle is already in degrees
MAT 170 Test 3 Form A Solutions (Fall 2011)
E. none of the above