Mathematics 2204
Final Review
Chapter 4
1.
Trigonometry 2
Which of the following angles is coterminal with 65 ?
245
(A)
2.
If sin
40o ,140o
140o , 220o
(C)
(B)
(D)
(C)
115°
1
The graph of y
2 cos x 1
(B)
3
3
(D)
295°
to the nearest degree if 0
360 ?
40o ,320o
220o ,320o
What is the exact value, in simplest form, of the expression
(A)
4.
65°
0.6428 , what are the values of
(A)
3.
(B)
(C)
1
cos 210
?
sin 30
(D)
3
2cos x 1 is provided below. What are the solutions of the equation
3?
y
2
(A)
(B)
(C)
(D)
x 180 k , k I
x 360 k , k I
x 90 360 k , k I
x 180 360 k , k I
1
- 720 °
- 540 °
- 360 °
- 180 °
180 °
360 °
540 °
720 °
-1
-2
-3
-4
5.
The point 1,0 on the unit circle is rotated 200°. What are the coordinates of the new
point?
0.9397, 0.3420
(A)
0.3640, 0.3420
(C)
6.
What is the value of
(A)
7.
Simplify:
(A)
30°
1
y2
if cos
0.3420, 0.9397
(B)
(D)
3
and 0
2
0.9397,0.3640
180 ?
(B)
120°
(C)
150°
(D)
(B)
2
y2
(C)
1 3y
y2
(D)
210°
3
y
2
y
y 3
y3
x
8.
What are the restrictions of the expression
(A)
(C)
9.
in if cos
(A)
10.
1
11.
x
x
0.1736 and sin
(B)
2
0, x
3, x
3
6
0.9848 ?
(C)
3
(D)
4
(C)
210°
(D)
240°
5
in degrees?
6
What is the value of
(A)
?
4x x 3
(B)
(D)
x
3, x 0
x 3, x 4
What quadrant is
x 6
120°
(B)
150°
In the circle given below, the central angle measures
6
and the radius is
5.6 cm. What is the length of arc x in centimetres?
5
(A)
(B)
(C)
(D)
0.9
2.9
33.6
168.0
(A)
cm
6
Which of the following is equivalent to sec
12.
.6
1
cot
cot
(B)
sin ?
(C)
tan
(D)
tan 2
13. Which angle is coterminal with 480°?
(A)
120 °
(B)
60°
(C)
120°
(D)
300°
14. In which quadrants of the unit circle is sine negative?
(A)
1 and 2
(B)
15. What is the exact value of
(B)
2
(A) 20°
(B)
(C)
2 and 3
(D)
sin 135
?
cos 240
(B)
16. What is the value of
1 and 4
2
4
(C)
2
4
2
(D)
3
in degrees?
2
240°
(C)
270°
(D)
540°
3 and 4
x
17. What is/are the restriction(s) of the expression
a.
b.
c.
d.
x
6, x
1
x
6, x 6
x
1
x 1, x 6
18. What is the simplified form of
a.
19. If sec
x 6 x 6
?
x 6 x 1
x 5
4x
3x 5
3x
b.
2 and 0
a. 30°, 150°
x 1 4
?
x
3x
c.
360 , what are the values of
b.
30°, 330°
c.
20. In the circle below, the central angle is
3
3x 7
3 x d.
x 5
3x2
?
60°, 120°
d.
and the length of the intercepted arc is 12.6cm.
What is the radius, in centimetres, of the circle?
(B)
13.2
(C)
24.0
(D)
a. 12.0
21. The graph of y 12.6
sin 0.5x
2 sin 0.5x
1 for 720
60°, 300°
26.4
1 is provided below. What are the solutions of the equation
3
x 720 ?
y
a.
b.
c.
d.
1260 , 540 ,180 ,900
720 , 360 ,0 ,360 ,720
360 ,0 ,360
540 ,180
x
22. The point 1,0 on the unit circle is rotated 300 . What are the coordinates of the new
point?
3 1
,
2
2
a.
23.
(B)
1
,
2
3
2
(C)
1 3
,
2 2
(D)
3 1
,
2 2
What is the simplified form of sin 2 cot 2 sec ?
(A)
cos
(B)
cos 2
sin
(C)
sin 4
cos3
(D)
sin
24.
2
?
2
What are the solutions of the equation sin x
(A)
b.
25.
x
45 360 k , k I
135 360 k , k I
(B)
x
45 360 k , k I
315 360 k , k I
x
135
225
(D)
x
225
315
360 k , k I
360 k , k I
360 k , k
360 k , k
I
I
What is the simplified form of the expression below?
x2 6 x 5
x 2
x 1 x 3
x 5
(A)
x 1
x 2
(B)
x 5
x 1
2
x 3 x 5
(D)
x 1
(C)
x 5
x 2
2
The point Q(1, 0) on a unit circle is rotated 210 about the origin. What are the new
coordinates of point Q?
26.
3
,
2
A)
27.
1
2
3 1
,
2 2
B)
3
,
2
C)
1
2
D)
3 1
,
2 2
Which of the following pairs of angles are coterminal?
A) 65 and 295
28. Which quadrant is
A) I
B) 45 and 45
located if cos
B) II
C) III
C) 120 and 240
is positive and sin
B) 1
30. What is the value of
A) 30 and 150
C)
if sec
cos 120
2 1
2
D)
2 and 0
3
5
B)
360 ?
B) 30 and 330
5
6
C)
C) 60 and 240
5
3
32. Which of the following is equivalent to
A) cos
B) sin
C)
D) 300
tan
sec
cos 2
sin
?
2 2 1
2
31. What is the value of 300 as a radian measure ?
A)
is negative ?
D) IV
29. What is the exact simplest form of sin 2 135
A) 0
D) 180 and 360
?
D)
sin
cos 2
D) 60 and 300
33. What are the restrictions on the domain of the following rational expression
( x 2)( x 3)
?
( x 2)( x 3)
A)
B)
3
34. The graph of y
C) 3
3, 2
D) 2, 3
4sin( x 90 ) 2 is given below. What are the solutions of the
equation 4sin( x 90 ) 2
2?
y
10
8
A) x 180 k , k
I
B) x
I
360 k , k
6
4
C) x 180
180 k , k
I
D) x 180
360 k , k
I
2
°
- 720
- 540
°
- 360
°
- 180
°
-2
180
°
360
°
540
°
720
°
x
-4
-6
-8
- 10
35. The length of an arc of a circle intercepted by a central angle of
2
radians is
3
15
15 cm. What is the radius of the circle to the nearest tenth of a centimetre?
A) 3.2
B) 7.2
C) 28.7
D) 31.4
2
3
O
36. What is the simplest form of
A) b
B)
b
a
1
a
1
?
b
C)
b 1
a b
D)
37. Which of the following is equivalent to 1 tan 2
A) cot 2
B) csc2
38. Solve csc x
A) 90
1
0 where 0
B) 0 , 90
C) tan 2
b2 a
ab
?
D) sec2
x 360
C) 90 , 270
D) 180 , 270
PART II:
1.
Simplify the following expression, expressing your answer in EXACT simplest form:
3sin 225 cos 135
2.
cm
cos 330
Simplify the following expression and list all restrictions:
5
3
x 1
x 2
x
3.
Solve 2sin x
4.
Prove:
2
sec2
0 where 0
x
sec2 sin 2
1
360 .
5.
Prove : sin
cos2
sin
6.
Solve 2 cos
3 0 where 0
7.
Find the EXACT value for the following expression :
csc
tan(60 )
8.
360
cot(60 )
Simplify the following expression:
1
x 2
3
2
x
2
2x
9.
Prove: sec
1 sin 2
cos .
10.
Prove: sec
1 sin 2
cos .
11.
Simplify the following expression, expressing your answer in EXACT simplest form:
sin120 cos 45
12.
cos 240 sin 90
Simplify the following expression, listing all restrictions:
2y 6
y2 9
y 2 2 y 15
3 y 15