Precalculus A Semester Exam Review Answers 2015-2016

PRECALCULUS A
Semester A Review Answers
Precalculus A
Semester Exam Review Answers
2015-2016
MCPS © 2015–2016
PRECALCULUS A
1.
2.
B
3.
a.
jump
b.
infinite
c.
removable
18
5
4.
c
5.
c9
6.
B
7.
even function
8.
odd function
9.
a.
odd
b.
even
c.
neither
10.
C
11.
a.
 4, 2    2,3
b.
 1,3
MCPS © 2015–2016
Semester A Review Answers
PRECALCULUS A
12.
13.
Semester A Review Answers
a.
f 1  x   x 2  2, x  0
b.
f 1  x   3 x  4
a.
True
b.
False
14.
B; C; A; D
15.
A
y
16.
x
y
x
y
x
r
r
, cos   , tan   , cot   , sec   , csc  
r
r
x
y
x
y
17.
sin  
18.
3
4
3
5
5
cos   , tan    , cot    , sec   , csc   
5
3
4
3
4
19.
a.
quadrant 2
b.
quadrant 3
c.
quadrant 4
a.
2
9
b.
11
12
20.
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PRECALCULUS A
21.
22.
Semester A Review Answers
a.
sin   0.6
b.
cos   0.8
c.
tan  
3
 0.75
4
Check graphs in your text.
23. sine, cosine, secant and cosecant have periods of 2 . Tangent and cotangent have periods of 
24.

8
25.
b6
26.
c
27.
a.
1
2
b.

e.
1
f.
undefined
i.
1
2
j.
m.
 2
n.

5
1
2
c.
 3
d.
1
g.
1
h.

1
2
k.

3
2
l.
1
3
 3
o.

2
3
p.
1
1
2
28.
Domain
Range
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Sin 1 x
1  x  1
Cos 1 x
1  x  1

0 y 

2
 y

2
Tan 1 x
All real numbers


2
 y

2
PRECALCULUS A
29.
30.
31.
32.
Semester A Review Answers
a.
inverse tangent
b.
inverse sine
c.
inverse cosine
a.

b.
6

3
4

d.

g.

j.
1
2
k.

m.
5
8
n.
12
5
a.
y  3  2sin x
b.

y  3sin 
2
c.


y  2  4 cos  x  
6

e.
3

h.
2

x

 
 
y  3sin   x   
2 
3
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c.
3

2
1
2

3

f.

i.
0
l.
1
o.

6
4
PRECALCULUS A
33.
a.
Semester A Review Answers
2

; phase shift right; vertical translation 5 up
6
3
y
amplitude 2; period
7
5
3
0
b.



6
3
2
2
3
5
6
x
amplitude 5; period 2; phase shift 1 left; no vertical translation, x-axis reflection
y
5
1

–5
MCPS © 2015–2016
1
2
1
2
1
x
PRECALCULUS A
33.
c.
Semester A Review Answers


amplitude 1; period ; phase shift
right; vertical translation 2 down.
2
4
y

0
3
8
4

5
8
2
3
4
–1
–2
–3
34.
35.
36.
4
7
a.
sin 34o
b.
cos
c.
sin 4
d.
tan 36o
e.
cos
f.
cos 3
g.
cos11.5o
h.
sin
a.
sin  2 A  
b.
cos  2 A  
d.
5
 A
cos   
26
2
a.
  225o , 315o
b.
  120o , 240o
2
9
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120
169
12
13
119
169
c.
1
 A
sin   
26
2
x
PRECALCULUS A
37.
a.
x
b.
x
Semester A Review Answers
3 7
,
4 4
  5
, ,
6 2 6
38.
Radius
6 inches
Angle (radians)

18 feet
10 meters
39.
Arc length
3
inches
2
15 feet
4
5
6
3
30 meters
The identity proofs shown below transform the left hand side into the right hand side.
a.
b.
 sin x  cos x 
sin  cot 
cos 
sin  
sin 
cos 
c.
2
sin 2 x  2sin x cos x  cos 2 x
 sin
2
x  cos 2 x   2sin x cos x
1  sin  2 x 
d.
csc x
1  cot 2 x
csc x
csc 2 x
1
csc x
sin x
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sin  cos 

cos  sin 
sin 2   cos 2 
cos  sin 
1
cos  sin 
sec  csc 
PRECALCULUS A
Semester A Review Answers
39.
e.
f.
sin 2   sin 2  tan 2 
40.
sin  x  y   sin  x  y 
sin 2  1  tan 2  
 sin x cos y  cos x sin y    sin x cos y  cos x sin y 
sin 2  sec 2 
2sin x cos y
sin 2 
cos 2 
tan 2 
d
a.
160
20
0
41.
b.
 
d  90  70 cos  t 
3 
c.
125 cm
d.
2.260 seconds
a.


h  50  30 cos   t  3 
4

b.
77.716 feet
c.
t  1.929, 4.071
MCPS © 2015–2016
3
6
t
PRECALCULUS A
42.
a.
Semester A Review Answers
d
8
5
2
0
43.
6.5
13
b.
 2 
d  5  3cos 
t
 13 
c.
t  1.740 hours after midnight or about 1:44/1.45 a.m.
a.
  131.810o , 228.190o
b.
  199.471o , 340.529o
44.
no triangles
45.
b  16.915cm
46.
mB  47.9o
47.
There are two possible triangles:
Triangle 1: mB  72.2o , mC  49.8o , c  10.3
Triangle 2: mB  107.8o , mC  14.2o , c  3.3
48.
285.630 ft.
49.
643.470 ft.
50.
31.114 ft.
51.
5.698 miles
52.
10
MCPS © 2015–2016
t
PRECALCULUS A
53.
54.
a.
224.816 feet
b.
17,658.952 square feet
c.
$22,702.05
1,917.028
MCPS © 2015–2016
Semester A Review Answers