290
Chapter
4
Trigonometry
VOCABUTARY CHECK: Fiil in the btank.
1.
means "measurement of triangles.',
2. An
3.
_is
determined by rotating a ray about its endpoint.
Tivo angles that have the same initial and terminal sides
are
-
4' one
5' Angles
are
6'
is the measure of a central angle that intercepts an arc
equal to the radius of the circle.
that measure between
_
0
and
t/2are
angles, and angles that measure between
angles.
Two positive angles that have a sum of
have a sum
of
r are--
angles.
rf2 are
rf2
and,
n
angles, whereas two positive angles that
-
7. The angle measure that is equivalent to
166! of a complete revolution about an angle,s vertex is one
8. The
speed of a particle is the ratio of the arc length traveled
to the time faveled.
9. The
speed of a particle is the ratio of the change in the
central angle to time.
L0.
sector of a circle with radius r and central angle
o,where 0 is measured in radians, is given by
"
ffi"rffi#
-
ln Exercises 1-fl,estimate the angle to the nearest
one-half
radian.
ln Exercises I3-r 6, sketch each angle in standard position.
L3. (a)
15. (a)
5rr
(b)
4
llrr
-T
(b)-3
6
14.(a)
-T o) T
1,6.(a)4
(b)7r
ln Exercises 17-20, determine two coterminat angles (one
positive and one negative) for each angle.
Give your
3.
answers in radians.
17. (a)
(b)
6'6
s'/
4-
3n
ln Exercises 7-12, determine the quadrant in which
angle lies. (The angle measure is given in radians.)
7.(a); o)+ 8.(a)f
s. (a) -# o) -2
(b)
2
each
L8.
(a)
7t
2
T
3n
10. (a)
-1
3.5 (b) 2.25
12. (a) 6.02 (b) - 4.25
11. (a)
2
(b)
\/g -llrr
19. (a)
e:U
ft) 0:! t2
3
20. (a) 0 _ _9rr
4
(b)
e- -2rr
15
ln Exercises 21'24,find (if possible) the complement and
4L. (a)
0:240"
supplement of each angle.
42. (a)
0-
:3
(b)
T
22. (a)
(a) 1
(b)
2
24. (a)
21. (a)
23.
TT
12
3
(b) llrr
,/L
26.
L/-
18o
45. (a) J9"
(b)
(b)
43. (a)
angle.
,,^,
-420"
00:
-180"
230'
supplement of each angle.
1.s
ln Exercises 2s-3},estimate the number of degrees in the
25.
(b)
(b)
ln Exercises 43-46, find (if possible) the complement and
n
(b)
291
Radian and Degree Measure
Section 4.1
3o
115"
44. (a)
150"
46. (a) 130'
(b) &"
(b)
170'
ln Exercises 47-s},rewrite each angle in radian measure as
a multiple of rr. (Do not use a calculator.)
\\
30o (b) 150"
49. (a) -20" (b) -240o
47. (a)
315" (b) 120"
-n0' 0) l$o
48. (a)
50. (a)
ln Exercises 51-54, rewrite each angle in degree measure.
(Do not use a calculator.)
T
s3. (a)
+
sl.
30.
29.
-:
(a)
+
O) -X
tu)
s2- (a)
s4. (a)
7rr
_T
(b) o,
Llrr
(b)T
6
convert the angle measure from
to three decimal places.
Round
radians.
to
degrees
ln Exercises 55-62,
ln Exercises 3l-34,determine the quadrant in which each
angle lies.
31. (a)
32. (a)
8.3o
33. (a)
-
34. (a)
-zffi"
57. -216.35"
(b) 285'
(b) 257o 30'
130'
59.
6L.
(b) -336'
(b) -3.4"
132" 50'
55. 1 15'
532"
- 0.83"
30"
37. (a) 405'
(b)
150"
(b)
480"
-n0' O) 38. (a) -750" (b) - 600o
36. (a)
120'
ln Exercises 39-42, determine two coterminal angles (one
positive and one negative) for each angle. Give your
answers in degrees.
39.
(a)
40. (a)
(b)
62. 0.54"
ln Exercises 63-T},convert the angle measure from radians
to degrees. Round to three decimal places.
ln Exercises 35-3g, sketch each angle in standard position.
35. (a)
56. 87.4"
58. - 48.n"
60. 345"
63.
64'
;
15n
65'
5n
11
66-ry
8
67.
- 4.2r
68. 4.8rr
69.
-2
70. -0.57
ln Exercises 71-74,convert each angle measure to decimal
degree form.
71. (a) 54" 45'
(b)
72. (a) 245" l0'
73. (a) 85" 18' 30'
74. (a) - 135' 36'
(b) 2o 1.2'
(b) 330'25o
-
(b) -
t28" 30'
408" L6',20',
ln Exercises 75-78,convert each angle measure to Do M'S"
form.
75. (a) 240.6"
(b)
76. (a) -345.12"
77. (a) 2.5"
(b) 0.45'
78. (a) - 0.355"
(b) 0.7865"
-
145.8"
(b) - 3.58'