Download Slide 4- 1 Homework, Page 439 Chapter Review

Homework, Page 439
Chapter Review
Determine the quadrant of the terminal side of an angle in standard
position. Convert degree measures to radians and radian measures
to degrees.
1. 5
2
5 4 

  positive y -axis
2
2
2
5 180
 450
2 
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Slide 4- 1
Homework, Page 439
Chapter Review
Determine the quadrant of the terminal side of an angle in standard
position. Convert degree measures to radians and radian measures
to degrees.
5. 78
0  78    Quadrant

13
78


30
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Slide 4- 2
Homework, Page 439
Chapter Review
Determine the angle measure in both degrees and radians. Draw the
angle in standard position if its terminal side is obtained as
described.
9.
A three-quarters counterclockwise rotation

270 
radians

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270 degrees
Slide 4- 3
Homework, Page 439
Chapter Review
The point is on the terminal side of an angle in standard position.
Give the smallest positive angle measure in both radians and
degrees.
-1
13.
1, 3




1, 3  tan  


3
 3
1
sqrt(3)

  tan 1  3  60  180  120
2
  120
3
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Slide 4- 4
Homework, Page 439
Chapter Review
Evaluate the expression exactly without a calculator.
sin 30
17.
sin 30 
1
2
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Slide 4- 5
Homework, Page 439
Chapter Review
Evaluate the expression exactly without a calculator.
5
21.
sin
sin
6
5 1

6 2
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Slide 4- 6
Homework, Page 439
Chapter Review
Evaluate the expression exactly without a calculator.
25. cos 270
cos 270  
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Slide 4- 7
Homework, Page 439
Chapter Review
Evaluate exactly all six trigonometric functions of the angle.

29.

6
1
 
 
sin       csc     2
2
 6
 6
2 3
3
  2
 

 sec    
cos    
3
3
 6
 6 2
1
3
1
 
 
2
 cot      3


tan     
3
3
3
 6
 6
2
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Slide 4- 8
Homework, Page 439
33.
c
Chapter Review
Find all six trigonometric functions of α in ΔABC.
 5
2

  2   13
2
5
13
sin     csc   
13
5
12
13
cos   
 sec   
13
12
5
12
tan   
 cot   
12
5
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
B
5 cm

A
12 cm
C
Slide 4- 9
Homework, Page 439
Chapter Review
3
37.
Solve for x in radians tan x  1.35 if   x 
2
tan 1 1.35  4.075 radians
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Slide 4- 10
Homework, Page 439
Chapter Review
Solve the right ΔABC.
41.   48 a  
  48 a  
c

B
a

A
        
b
C
b
tan    b  a tan   7 tan 48  b  
a
a
a
7
cos    c 

 c  10.461
c
cos  cos 48
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Slide 4- 11
Homework, Page 439
Chapter Review
x is an angle in standard position with 0  x  2 . Determine the
quadrant of x.
sin x  0 and tan x  0
45.
sin x  0 and tan x  0  Quadrant III
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Slide 4- 12
Homework, Page 439
Chapter Review
Point P is on the terminal side of angle θ. Evaluate the six
trigonometric functions for θ.
49.  3,6 
 3, 6   c 
a b 
2
2
 3 
2
  6   45  3 5
2
6
2 5
5
sin x 

 csc x 
5
2
3 5
3
5
cos x 

 sec x   5
5
3 5
6
1
tan x 
 2  cot x  
3
2
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Slide 4- 13
Homework, Page 439
Chapter Review
Use transformations to describe how the graph of the function is
related to a basic trigonometric graph. Graph two periods.
53. y  sin  x   
The graph of y  sin  x    is obtained from the graph
of y  sin  x  by translating  units to the left.
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Slide 4- 14
Homework, Page 439
Chapter Review
Use transformations to describe how the graph of the function is
related to a basic trigonometric graph. Graph two periods.
57. y  tan  2 x 
The graph of y  tan  2 x    is obtained from the graph
1
of y  tan  x  by applying a horizontal shrink of .
2
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Slide 4- 15
Homework, Page 439
Chapter Review
State the amplitude, period, phase shift, domain, and range of the
sinusoid.
61. f  x   2sin  3x 
2
f  x   2sin  3x   p 
3
2
Amplitude:2; Period: ; Phase shift: None
3
Domain: all real numbers; Range:  2  y  2
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Slide 4- 16
Homework, Page 439
Chapter Review
State the amplitude, period, phase shift, domain, and range of the
sinusoid.
65. f  x   4cos  2 x  1
 
1 
f  x   4cos  2 x  1  f  x   4cos  2  x   
2 
 
2
p

2
1
Amplitude:4; Period: ; Phase shift: +
2
Domain: all real numbers; Range:  4  y  4
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Slide 4- 17
Homework, Page 439
Chapter Review
Evaluate the expression, in both degrees and radians.
69.
sin 1  0.766 
sin 1  0.766   0.873 radians
0.873
180

 49.996
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Slide 4- 18
Homework, Page 439
Chapter Review
Use transformations to describe how the graph of the function is
related to a basic inverse trigonometric graph. State the domain and
range.
1
73. y  sin  3 x 
To obtain the graph of y  sin 1  3x  from the graph of
y  sin 1  x  apply a horizontal shrink of 1 .
3
1
1


Domain : x :   x  ; Range : y :   y 
3
3
2
2
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Slide 4- 19
Homework, Page 439
Chapter Review
Find the exact value of x without using a calculator.
77. sin x  0.5,   x  
2
sin 1 0.5  
6
 
6
 5
6
or 150
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Slide 4- 20
Homework, Page 439
Chapter Review
Find the exact value of x without using a calculator.
81. csc x  1, 0  x  2
1
csc x 
 1  sin x  1  sin 1  1  3
2
sin x
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Slide 4- 21
Homework, Page 439
Chapter Review
Evaluate the expression without a calculator.
85. tan tan 1 1




tan tan 1 1  1
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Slide 4- 22
Homework, Page 439
Chapter Review
Determine whether the function is periodic. State the period, if
applicable, the domain, and the range.
89. f  x   sec x
f  x  is a periodic function
Period: 
Domain : x : x 

2
 n
Range: y : y  1
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Slide 4- 23
Homework, Page 439
Chapter Review
93.
Find the length of the arc intercepted by a central angle of
2π/3 rad in a circle of radius 2
s
2
4
   s  r  2

r
3
3
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Slide 4- 24
Homework, Page 439
Chapter Review
97.
From the top of a 150-ft tall building, Flora watches a car
moving towards her. If the angle of depression changes from 18º to
42º during the observation, how far does the car travel?
150
150
tan  
 distance 
distance
tan 
150
150
d1 
 461.653  d 2 
 166.592
tan18
tan 42
d1  d 2  295.061 ft
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Slide 4- 25
Homework, Page 439
Chapter Review
101. On flat ground, 62–ft from the base of a tree, the angle of
elevation of the tree top is 72º24‘. What is the height of the tree?
24
  72.4
60
h
tan 72.4 
 h  62 tan 72.4  195.449 ft
62
7224  72
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Slide 4- 26
Homework, Page 439
Chapter Review
105. The average daily air temperature (ºF) in Fairbanks from
1975 to 2004 can be modeled by the equation
 2

T  x   37.3sin 
 x  114   26
 365

where x is time in days with x = 1 representing January 1. On what
days do you expect the average temperature to be 32ºF?
On days 123 (May 3) and 287 (October 14), we would expect the
average temperature to be 32ºF.
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Slide 4- 27