# 2015-2016 Honors Precalc A JANUARY Review KEY

```HONORS PRECALCULUS A
Honors Precalculus A
2015-2016
MCPS &copy; 2015–2016
HONORS PRECALCULUS A
1.
2.
B
3.
a.
jump
b.
infinite
c.
removable
4.
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HONORS PRECALCULUS A
5.
lim f  x   8
a.
x  4
lim f  x   k , where k is any real number other than 8
b.
x  4
6.
B
7.
c
8.
c9
9.
even function
10.
odd function
11.
a.
odd
b.
even
c.
neither
d.
even
18
5
12.
C
13.
a.
 4, 2    2,3
b.
 1,3
a.
f 1  x   x 2  2, x  0
b.
f 1  x   3 x  4
c.
f 1  x  
14.
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2x  4
, x 1
x 1
HONORS PRECALCULUS A
15.
a.
b.
y
O
16.
a.
True
b.
False
17.
B; C; A; D
18.
A
19.
O
x
y
x
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y
x
HONORS PRECALCULUS A
20.
a.
Stretch vertically by a factor of two, translate one unit right and three units down.
b.
y
O
 5, 6
c.
5  x  6 or
d.
9  g  x   5 or
 9,5
21.
B
22.
a.
y   17,  4,  3
b.
No, for some x in the domain there are two values of y.
c.
f  x   17  x , g  x    17  x
23.
sin  
y
x
y
x
r
r
, cos   , tan   , cot   , sec   , csc  
r
r
x
y
x
y
24.
3
4
3
5
5
cos   , tan    , cot    , sec   , csc   
5
3
4
3
4
MCPS &copy; 2015–2016
x
HONORS PRECALCULUS A
25.
26.
27.
28.
29.
a.
b.
c.
a.
2
9
b.
11
12
a.
sin   0.6
b.
cos   0.8
c.
tan  
a.
1
2
b.

e.
1
f.
undefined
i.
1
2
j.
m.
 2
n.
3
 0.75
4
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
30. sine, cosine, secant and cosecant have periods of 2 . Tangent and cotangent have periods of 
31.

8
32.
b6
33.
c

5
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HONORS PRECALCULUS A
34.
Sin 1 x
1  x  1 or
Domain
Range
35.
36.
37.
38.


2
 y

  
or   , 
2
 2 2
a.
inverse tangent
b.
inverse sine
c.
inverse cosine
a.

 1,1
b.
6

3
4

g.

j.
1
2
k.

m.
5
8
n.
12
5
a.
y  3  2sin x
b.
 
y  3sin  x 
2 
c.


y  2  4 cos  x  
6

3

2
 
 
y  3sin   x   
2 
3
MCPS &copy; 2015–2016
e.
h.
3

2
1
2
0,  
0  y   or
c.

d.
Cos 1 x
1  x  1 or  1,1

3

f.

i.
0
l.
1
o.

6
4
Tan 1 x
All real numbers


2
 y

  
or   , 
2
 2 2
HONORS PRECALCULUS A
39.
a.
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
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1
2
1
2
1
x
HONORS PRECALCULUS A
39.
c.


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
40.
D
41.
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.
 A 1
tan   
2 5
e.
5
 A
cos   
26
2
a.
  225o , 315o
b.
  120o , 240o
42.
43.
2
9
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120
169
4
7
12
13
119
169
c.
1
 A
sin   
26
2
x
HONORS PRECALCULUS A
44.
a.
x
b.
x
c.
x
 2 4 5
3
,
3
,
3
,
3
  5
, ,
6 2 6
7 11 19 23
,
,
,
12 12 12 12
45.
6 inches
Arc length
3
inches
2
15 feet

18 feet
10 meters
4
5
6
3
30 meters
46.
one triangle
47.
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 
HONORS PRECALCULUS A
47.
e.
f.
sin 2   sin 2  tan 2 
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 
g.
h.
tan x  cot x
sin x cos x

cos x sin x
sin 2 x  cos 2 x
sin x cos x
1
1
sin  2 x 
2
2 csc  2 x 
48.
1.68  5.278 m/s
49.
a.
b.

40
2200
 2303.835ft/sec
3
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cot  sec 

cos  cot 
cot 2   cos  sec 
cos  cot 
2
cot   1
cos  cot 
csc 2 
cos 
cos  
sin 
2
csc 
cos 2  csc 
csc  sec 2 
HONORS PRECALCULUS A
50.
d
a.
160
20
0
51.
52.
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 sec , 4.071 sec
a.
3
6
t
d
8
5
2
0
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.
MCPS &copy; 2015–2016
t
HONORS PRECALCULUS A
53.
a.
  131.810o , 228.190o
b.
  199.471o , 340.529o
54.
no triangles
55.
b  16.915cm
56.
mB  47.9o
57.
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
58.
285.630 ft.
59.
643.470 ft.
60.
31.114 ft.
61.
5.698 miles
62.
10
63.
a.
224.816 feet
b.
17,658.952 square feet
c.
\$22,702.05
64.
1,013.253
65.
mA  36.9o , 143.1o
MCPS &copy; 2015–2016