34.
18. cos (!450°) " cos (!450 # 720)°
" cos 270°
"0
19. sin (!180°) " sin (!180 # 360)°
" sin 180°
"0
13%
13% # 4%
20. sin !$
$ " sin !$
$
!
"
6
"
! 6
11%
sin !$
$
6 "
2
9%
$$
2
" cos
45˚
"1
"
x"
1
1
$$ # $$
2
2
$
2
2
38. A!1 " $1$
#3
$
#3
$
!$
$ # 2!$$"
!
2 "
2
4 sin 300° # 2 cos 30°
$$$ " $$$
4
26.
27.
12 ! 5
3
3
" $1$
7
!2#3
$ # #3
$
" $$
3
#3
$
" !$
$
3
#3
$
sin 30° # cos 60° " $1$ # $
$
2
2
1 # #3
$
"$
2
2
2
#3
$
1
(sin 60°)2 # (cos 60°)2 " $
$ # $$
2
2
" $3$ # $1$
4
4
! "
39.
!"
32.
0.75
1
r " #x$2$#
$$y2$
8.
3 " #2
$2$#
$$y2$
2
9"4#y
5 " y2
#5
$ "y
#5
$
sin Cos!1 $2$ " $
$
t
!
h
3
O
!3
1
2
3
4
9.
t
! 3 ""
4
$$
5
10.
13. 90°
1
$$
2
3
11. !45°
12.
1
$$
2
14. sin ' " $8$
16
33. a2 " 752 # 3002 ! 2(75)(300) cos 15°
a2 % 52158.34
a % 228.4; 228 miles
sin ' " $1$
2
' " sin!1
' " 30°
© Glencoe/McGraw-Hill
(2, !2)
1. They are inverses of each other.
2. The trigonometric functions are not one!to!one
functions.
3. Restricted domains are denoted with a capital
letter.
4. ' " Arcsin x
5. y " Arctan ! 3
6. 0°
7. 45°
19
0.5
x # 2y " !2
2 # 2y " !2
2y " !4
y " !2
Page 813 Check for Understanding
!$#2$3$ "!!$12$"
29. See students’ work.
30.
sine: D " {all reals}, R " {!1 & x & 1}
cosine: D " {all reals}, R " {!1 & x & 1}
tangent: D " {all reals except 90, 270, . . .},
R " {all reals}
31.
h
0.25
!5
& !4
!1 !3 '
Inverse Trigonometric
Functions
13-7
" !2#3
$
O
!19
!5
& !4
!1 !3 '
x # 2y " !2
(#)3x ! 2y " 10
4x " 8
x"2
"1
28. 8(sin 120°)(cos 120°) " 8
log 24
$
log 4
x % 2.2925
37. x4 ! 13x2 # 36 " 0
(x2)2 ! 13(x2) # 36 " 0
(x2 ! 9)(x2 ! 4) " 0
(x # 3)(x ! 3)(x # 2)(x ! 2) " 0
x # 3 " 0 or x ! 3 " 0 or x # 2 " 0 or x ! 2 " 0
x " !3
x"3
x " !2
x"2
!$12$"!$12$"
" $1$
25.
x
O
35. No, the figure is not self-similar.
36.
4x " 24
log 4x " log 24
x log 4 " log 24
!$92%$ ! 2%"
sin 30° # cos 60°
$$$
2
1
"
" cos $%$
2
"0
23. 4(sin 30°)(cos 60°) " 4
24.
x
!1
"$
$ or !1
135˚
!1
" !$1$
2
21. sin $3%$ " !1
22. cos
!2
1
tan 135° " $y$
y
367
1
$$
2
Algebra 2 Chapter 13
Pages 813–814 Exercises
15. b " Arccos a
46.
16. y " Arcsin x
17. ( " Arctan )
18. Arcsin
19. Arccos y " 45°
20. Arctan
21. 90°
22. 45°
25. 30°
26. 45°
29. 0°
30.
r " #x$2$#
$$y2$
23. 30°
27. 120°
7 " #6
$2$#
$$y2$
49 " 36 # y2
13 " y2
#1
$3
$"y
#1
$3
$
tan Cos!1 $6$ " $
$
!
7
"
!
9
"
!$4$
3
! ""x
S
2
47. cos ' "
6
"
cos ' "
3
"
5
50.
2
5
36. $%$ or 90°
2
38. 30°
35. 3
37. 60°
39. r " #x$2$#
$$y2$
40.
! 2"
2
41. r " #x$2$#
$$y2$
r " #x$2$#
$$y2$
2 " #x$2$#
$$(!
$1$$
)2
2
4"x #1
3 " x2
#3
$ "x
#3
$
cos [Arcsin !$1$ ] " $
$
r " #1
$2$#
$$
#3
$2$
$
r " #1
$$
#$
3
r " #4
$
"2
cos (Tan!1 #3
$) " $1$
42. cos
&
! "
!
1
$$
2
!
cos!1 $3$
5
43. sin 2 sin!1
44. sin 2
'
#2
$
$$
2
#2
$
"$
$!
2
#2
$
"$
$!
2
#2
$
"$
$
2
2
10
* (2 # k)" (2 # 1) # (2 # 2) # (2 # 3) # (2 # 4)
k"1
& 20 !17 ' & 20 71 '
47
"& '
01
54. AA "
x!7"0
x"7
y
y"3
cos
%
$$
2
x
O
0
x!y"2
Chapter 13 Highlights
#3
$
"$
$
2
" % sin [2(53.13)]
Page 815 Understanding and Using the
Vocabulary
% sin 106.26
4
% 0.96 or $2$
© Glencoe/McGraw-Hill
x " 65 sin 70°
x % 61.1; 61.1 meters
0, 7
55. x # y * 2
y*3
y * !x # 2
" " sin 60°
45. See students’ work.
x
x
$$
65
3
12
#2
$
#$
2
%
Cos!1 $
$ ! $$
2
2
sin 70° "
0.2392 % k
53. x2 ! 7x " 0
x(x ! 7) " 0
x"0
or
r " #$$#
$$$
r " #2
$
cos (Tan!1 1) " $1$ or
12
1
$$
4
# (2 # 5) # (2 # 6) # (2 # 7)
# (2 # 8) # (2 # 9) # (2 # 10)
" 3 # 4 # 5 # 6 # 7 # 8 # 9 # 10
# 11 # 12
" 75
51.
y " nekt
52. center: (4, 9)
164 " 80e3k
radius: 2
2.05 " e3k
ln 2.05 " ln e3k
ln 2.05 " 3k lne
ln 2.05 " 3k
ln 2.05
$$ " k
y2
"
48. %
70˚
52 " #x$2$#
$$32$
2
25 " x # 9
16 " x2
4"x
cos Arcsin $3$ " $4$
!
' " 30°
' # x " 90°
30° # x " 90°
x " 60°
60° north of east
()
65 m
r " #$$#
$$$
34.
I
$$t
Io
49.
5
r " #x$2$#
$$y2$
!
())
E
1
$$
2
cos ' " 0.5
' " 60°
r " #3
$2$#
$$(#
$3$$
)2
r " #9
$$
#$
3
r " #1
$2
$
" 2#3
$
#3
$
1
sin Arctan $
$ " $$
7
x2
24 mi
24. 0°
28. $1$
!
2
' " Cos!1
48 mi
'
W
6 " #x$2$#
$$52$
2
36 " x # 25
11 " x2
#1
$1
$ "x
#1
$1
$
cot Sin!1 $5$ " $
$
33.
9 " #x$2$#
$$72$
2
81 " x # 49
32 " x2
4#2
$"x
4#$
2
cot Sin!1 $7$ " $
$
" 30°
r " #x$2$#
$$y2$
31.
6
r " #x$2$#
$$y2$
32.
1
$$
2
cos ' " $1$
N
1.
4.
6.
8.
false, coterminal
2. true
3. true
false, sec '
5. true
false, law of cosines
7. true
false, an angle that has its terminal side on an
axis where x or y is equal to zero
9. false, tan '
10. false, terminal
25
368
Algebra 2 Chapter 13