Download Pure Mathematics 30: Unit 1 Review Assignment

Math 30-1 Chapter 4 Review Assignment p.1
Math 30-1: Chapter 4 Review: The Unit Circle
1. Convert the following units to either radians or degrees. If converting to radians, give the
EXACT VALUE and an APPROXIMATE VALUE rounded to 2 decimal places.
4
15
a)
b) 300o
c) 
d) 495o
e) 5
3
4
2. Identify the coterminal angle(s) for each, given the restrictions.
a) 195o ,  180o    180o
c) 305o ,  90o    90o
b)
5
,  2    2
4
d)
3. Determine all angles that are coterminal with
17
,    
2
7
.
6
4. State the reference angle for the following angles.
7
13
7
a) 
b)
c) 
8
12
9
d)
31
2
e) 27
5. Draw the following angles in standard position.
a) 1.25 radians
4.01 radians
6. Mary is given the diagram at the right, showing an angle
rotation of 120°. The arc length of the sector is 40 cm.
Determine the radius of the circle, to the nearest centimeter.
5.38 radians
Math 30-1 Chapter 4 Review Assignment p.2
7. A circle with a radius, r, an arc length of 34π, (T1.9)
a
17
and two central angles of
and
is shown
15
15
at the right.
a) Determine the value of a.
b) Determine the length of the radius, to the nearest whole number.
8. Determine the measure of the central angle subtended by an arc of 11.3 m in a circle whose
radius is 22.6 m. Give your answer in radians rounded to 2 decimal places.
9. If the point P  0.2, k  lies on a circle with a radius of 1, then the exact value of k can be
expressed as  b . Determine the value of b to the nearest hundredth. (T2.3)
2

10. Determine the missing coordinate for point P  x,   in quadrant III on the unit circle.
3

 5 12 
11. On a unit circle, if the point P   ,  lies on the terminal arm of an angle in standard
 13 13 
position, what are the exact values of the 6 trigonometric ratios?
(T2.2)
Math 30-1 Chapter 4 Review Assignment p.3
8
3
12. Given that cot   , where    
, determine the exact value of sec . (T2.3)
5
2
13. Given that csc   
7
3
   2 , determine the exact value of the five remaining
, and
2
2
trigonometric ratios.
14. Given that the point  2,3 is on the terminal arm of  , determine the exact value of the six
trigonometric ratios.
(T3.4)
15. Determine the exact value of the following ratios..
 5 
 
a) sin   
e) csc 

 3 
 6
(T3.2)
i) sec  3 
 7 
b) cos 

 4 
 5 
f) sec 

 4 
 
 3 
j) sin 2    tan  
4
 4 
 
c) tan  
6
 
g) cot   
 2
 
 2 
k) tan    2sin 

2
 3 
 
d) cot  
3
h) csc   
 5
l) cos 
 6

2  
2  
  sec     4 cot  

 4
3
Math 30-1 Chapter 4 Review Assignment p.4
 3 1

2 2
,  and point B  
,
16. Point A 
 lie (T3.2)
2
2
2
2




on the terminal are of two different angles in
standard position. The angle,  , where
a
.
0     , can be expressed in the form
b
Determine the values of a and b.
17. Solve for  in the interval 0°    360° if sec 10  2  sec .
(T3.3)
18. Determine the general solution, in radians, for 4csc  3  11 . Leave your answer in exact
form.
(T3.8)
19. Solve 2 cos 2   cos   3 for  in the domain 0°    360°. (T3.8)
20. Solve 2sin 2   sin   1 for  in the domain 0    2 .
(T3.8)