Name: ___________________________________________ Date: _____________________________
BLM 4–8
Chapter 4 Test
4. Suppose tan2   tan   0 and 0    2.
What does  equal?
Multiple Choice
For #1 to #5, choose the best answer.
1. What is the exact value of csc
7
4
?
 2
A
2
B
12
and
13
cos   0.
B
5
12
C
5
12
D
12
5
  if P()
7
6
is the point at the intersection of the
terminal arm of angle  and the unit circle?
  3 1
, 
A 
2
 2
 1  3 
B  ,

 2 2 
 1 3 
D  ,

 2 2 
5
4
3
7
, ,
4
4
5. What is the general solution of the equation
2 cos   1  0 in degrees?
A 240  360n, 300  360n, n  I
B 60  360n, 300  360n, n  I
C 60  360n, 120  360n, n  I
D 120  360n, 240  360n, n  I
Short Answer
3. What are the coordinates of P
 3 1
, 
C 
 2 2
3 7 
,
4 4
D 0,
2. Determine tan  if sin  
12
5
B

4
2
A
 5
,
4 4
C 0, , ,
2
2
C  2
D
A
6. Convert to radian measure. State the method
you used to arrive at your solution. Use each
conversion method at least once. Give
answers as both exact and approximate
measures to the nearest hundredth of a unit.
a) 270
b) –540
c) 150
d) 240
7. Convert the following radian measures to
degree measure. State the method you used
to arrive at your solution. Use each
conversion method at least once. Give
answers as approximate measures to the
nearest hundredth of a unit.
a) 3.25
b) 0.40
c) 
7
4
d) –5.35
8. The minute hand of an analogue clock
completes one revolution in 1 h. Determine
the exact value of the angle, in radians, the
minute hand moves in 135 min.
Copyright © 2012, McGraw-Hill Ryerson Limited, ISBN: 978-0-07-073887-4
Name: ___________________________________________ Date: _____________________________
BLM 4–8
(continued)
9. Use the information in each diagram to
determine the value of the variable. Give
your answers to the nearest hundredth of
a unit.
a)
10. Determine the exact value of
sin 2
   2 cos (120) tan  .
5
6
7
4
11. Given that sin   0.3 and cos   0.5,
determine the value of tan  to the nearest
tenth.
12. If sin  
3
, determine all possible
2
coordinates of P() where the terminal arm
of  intersects the unit circle.
b)
 3 1 
13. If P() =  ,  , what are the
 2 2
 ?
coordinates of P  

2
Extended Response
14. Consider an angle of
c)
4
radians.
5
a) Draw the angle in standard position.
b) Write a statement defining all angles that
are coterminal with this angle.
15. The point (3a, 4a) is on the terminal arm
of an angle in standard position. State the
exact value of the six trigonometric ratios.
16. Solve the equation sec2   2  0,
    .
d)
17. Consider the following trigonometric
equations.
A 2 sin   3  0
B
2 cos   1  0
C 2 2 sin  cos   2 sin   6 cos   3  0
a) Solve equations A and B over the
domain 0    .
b) Explain how you can use equations A
and B to solve equation C, 0    .
Copyright © 2012, McGraw-Hill Ryerson Limited, ISBN: 978-0-07-073887-4
c) Example: unit analysis; 315°
d) Example proportion method;  306.53°
Chapter 4 Test Answers
1. C
2. A
3. A
4. C
5. D
6. a) Example: unitary method;
8.
9
2
9. a)   133.69 or 2.33 b) a  31.85 cm
c) r  6.99 m d) a  4.28 ft
3
;  4.71
2
b) Example: proportion method; 3;  9.42
5
;  2.62
6
4
d) Example: unitary method;
;  4.19
3
c) Example: unit analysis;
7. a) Example: proportion method;  186.21°
b) Example: unitary method;  22.92°
10.
3
4
11. 0.6
 1 3   1 3 
12.  ,
,  ,

 2 2  2 2 
1 3
13.  ,

2 2 
BLM 4–9
(continued)
14. a)
4
 2n, n  I
5
15. sin   4 , cos   3 , tan   4 ,
5
3
5
5

5

3
csc  
, sec   , cot  
3
4
4
 
16.  ,
4 4
 2

17. a) Equation A:   , ; Equation B:  
3 3
4
b)
b) Equation C is the product of Equation A times
Equation B (i.e., AB  C). Therefore, the solution to
Equation C is the solutions to A and B:  
  2
, ,
.
4 3 3
Copyright © 2012, McGraw-Hill Ryerson Limited, ISBN: 978-0-07-073887-4