Download Chapter 8 Solutions

Practice Workbook Answers
a. Since 210 is the same as 150 on
the unit circle,
sin 210 sin (150). Also, since
150 is in Quadrant III, where
sine is negative,
sin (150) sin 150.
So, sin 210 sin 150.
b. 30 forms a 30 angle with the
x-axis. 60 forms a 30 angle with
the y-axis. The triangle formed
when you drop an altitude from
30 on the unit circle to the x-axis
is congruent to the triangle formed
when you drop an altitude from
60 on the unit circle to the y-axis
by AAS. So, cos 30 sin 60.
Chapter 8
Lessons 8.2 and 8.3
Additional Practice
1. a.
y
120
x
O
sin 120 "23 , cos 120 212 ,
tan 120 2"3
b.
y
315
x
b. 2"23
3. a. 212
O
4. a. u 270 360 k, where k is an
integer.
b. u 180 360 k, where k is an
integer.
c. u 135 180 k, where k is an
integer.
sin 315 2"22 , cos 315 "22 ,
tan 315 1
c.
(continued)
y
240
5. a. cos (45) "22 , sin (45) 2"22,
tan (45) 1
b. cos (60) 1 , sin (60) 2"3 ,
x
O
2
tan (60) 2"3
sin 240 2"23 , cos 240 212 ,
tan 240 "3
d.
y
60
x
O
6. a. sin 55
c. sin 50
b. cos 80
d. cos 50
7. a. cos u
c. cos u
e. sin u
g. sin u
b. sin u
d. sin u
f. cos u
h. cos u
2
8. False; answers may vary. Sample:
Let a 60 and b 30. Then
sin (a b) sin 30 12 , but
sin 60 "23 , cos 60 12 ,
tan 60 "3
sin 60 sin 30 "23 12 12 .
Also, cos (a b) cos 30 "23 , but
2. a–b. Answers may vary. Samples
are given.
cos 60 cos 30 12 "23 "23 .
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Practice Workbook Answers
9. a. positive
c. negative
10. a. 315
b. negative
d. positive
b. 135
6. 270
7. 90, 270
c. 225
Lessons 8.7 and 8.8
Additional Practice
Lessons 8.4 and 8.5
Additional Practice
1. a. 60, 120
c. 60
(continued)
1. Answers may vary. Sample:
b. 150, 210
d. 210
1
2. a. Answers may vary. Sample:
60
60 120
240 300
y cos x
1
b. No; however, if sin u 0 and
The graph of sin u is a translation of
cos u by 90 to the left. So,
sin u cos (u 90).
1 1
tan2 u
cos2 u 1 cos2 u sin2 u sin2 u
sin2 u
sin2 u
2
2
cos u 1 sin u 1 .
sin2 u
sin2 u
2
sin2 30 cos2 30 Q 12 R a "23 b
x
O
1
1 1 1 2 A "2 B 2
tan2 458
1
a 2 b2 2 458 .
sin
"2
3. a. 0
b. 0
c. Answers may vary. Sample:
Let u 30.
y sin x
0.5
tan 45 1 and sin 45 "22 , so
cos u 0, then
y
2.
1
y
x
90
2
14 34 212 and
sin4 30 cos4 30 O
90
180
1
4
1 4 a "3 b 1 9 21 .
2
2
2
16
16
3. 66, 294
Q R
4. a.
d. sin4 u cos4 u Asin2 u cos2 uB
Asin2 u cos2 uB
(1)Asin2 u cos2 uB
Asin2 u cos2 uB
1
y
x
180
4. a. 210, 330
b. 45, 135, 225, 315
c. 135, 315
d. 135, 225
O
180
b. The graph of f (x) cos x is a
translation of g(x) cos x by
180 to the right or left.
5. a. 180, 360, 45, 135
b. 30, 150, 210, 330
c. 90, 270, 120, 240
d. 120, 240, 0, 360
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Practice Workbook Answers
Lesson 8.9 Additional Practice
5. Answers may vary. Sample:
sin x , and in Quadrant I both
tan x cos
x
sin x and cos x are the same sign, but
in Quadrant IV they have different
signs. So tan x is positive in Quadrant
I and negative in Quadrant IV.
1. C
2. cos (a b) cos a cos b sin a sin b
6. a.
y
3
2
1
x
O
90
90
(continued)
270
1
3. a. cos (180 u)
cos (180 (u))
cos 180 cos (u) sin 180 sin (u)
(1) cos u (0) (sin u)
cos u
b. sin (180 u)
sin (180 (u))
sin 180 cos (u) cos 180 sin (u)
(0) cos u (1) (sin u)
sin u
2
4. a. cos x
c. sin x
b. sin x
d. cos x
3
5. Answers may vary. Sample:
cos x 1 sin x
2cos x 1 sin x
b. 72, 252
tan x 1 tan y
c. 108, 288
6. tan (x y) 1 1 tan x tan y
7. a.
7. a. "23 cos u b. "22 cos u y
2
1
90
O
90
270
x
1
2
1 sin u
2
"2
2 sin u
c. 12 cos u "23 sin u
d. 212 cos u "23 sin u
e. 2"23 cos u 12 sin u
"2
8. #2 1
2
b. The graph of f (x) tan x is a
reflection of g(x) tan x over the
x-axis.
Lessons 8.11 and 8.12
Additional Practice
8. The graph of y tan x shows that it
is periodic with period 180, so
tan (180 x) tan x.
1. 135
2. C
3. a. 9 sin x cos x
b. 92 sin (2x)
c. sin (2x) 2 sin x cos x
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Practice Workbook Answers
(continued)
4. a. Any triangle with sides 10 and 12,
and an included angle of 30, is
congruent to nCAR by SAS. So,
there is only one such triangle.
b. 244 120 "3
5. Answers may vary. Sample: The sides
1, 1, and "2 are opposite the angles
with measures 45, 45, and 90, so
1
sin 458
"2
"2 and sin
"2.
908
6. a. 0.892
b. 63, 117
c. m/A 82 or 28; BC < 15.5 or 7.4
7. a. 0.369
b. 21
c. m/A 124; BC < 20.2
Lessons 8.13 and 8.14
Additional Practice
1. "1737
2. "274 2 210 cos F
3. 8 DE 22
4. a. If /U was the smallest angle, the
measures of angles T and B would
be greater than 80. However, the
sum of the angles in a triangle
cannot exceed 180, so /U cannot
be the smallest angle.
b. m/B 34
5. a. The angles opposite the sides
of length 9, 13, and 15 are 36.7,
59.5, and 83.8, respectively.
b. x < 4.57; h < 7.77
c. <58.275
6. a–b. 16 "3
7. A
8. Answers may vary. Samples: 5, 5, 8;
10, 10, 12; 10, 13, 13; 10, 10, 16
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