Appendix A Answers to Selected Exercises and Homework Problems
1 Triangles and Circles
1.1 Angles and Triangles
Homework 1.1
3.
Answer.
5.
Answer.
7.
Answer.
9.
Answer.
11.
Answer.
13.
Answer.
15.
Answer.
17.
Answer.
19.
Answer.
21.
Answer.
23.
Answer.
- An exterior angle is equal to the sum of the opposite interior angles.
25.
Answer.
27.
Answer.
29.
Answer.
- a right triangle
31.
Answer.
- They are base angles of an isosceles triangle.
- They are base angles of an isosceles triangle.
corresponds to of Problem 29, and corresponds to of Problem 29.
33.
Answer.
35.
Answer.
37.
Answer.
39.
Answer.
41.
Answer.
43.
Answer.
45.
Answer.
- In the equation
substitute for and substitute for to conclude that the sum of the angles in the triangle is
47.
Answer.
1.2 Similar Triangles
Homework 1.2
1.
Answer.
3.
Answer.
5.
Answer.

7.
Answer.
Similar. Corresponding sides are proportional.
9.
Answer.
Similar. Corresponding angles are equal.
11.
Answer.
13.
Answer.
15.
Answer.
17.
Answer.
19.
Answer.
21.
Answer.
154 feet
23.
Answer.
1 mile
25.
Answer.
17.1 square feet
27.
Answer.
29.
Answer.
31.
Answer.
33.
Answer.
35.
Answer.
37.
Answer.
39.
Answer.
and The hypotenuse is in in and in The short leg is in in and in The longer leg is in in and in
1.3 Circles
Homework 1.3
1.
Answer.
13 miles
3.
Answer.
10, 10.00
5.
Answer.
7.
Answer.
5
9.
Answer.
11.
Answer.
5
13.
Answer.
15.
Answer.
17.
Answer.
The distance between the points and is 3 units.
19.
Answer.
cm- 8.49 cm
21.
Answer.
sq in- 78.54 sq in
23.
Answer.
- approximation
- approximation
- approximation
- exact
25.
Answer.
27.
Answer.
29.
Answer.
31.
Answer.
- No real value of
can satisfy unless - The graph has no points where
and no points where
33.
Answer.
35.
Answer.
37.
Answer.
39.
Answer.
41.
Answer.
43.
Answer.
ft sq ft
45.
Answer.
sq ft ft
47.
Answer.
sq km km
49.
Answer.
sq m m
51.
Answer.
2070 miles
53.
Answer.
- 54,000 miles
- 2240 mph
55.
Answer.
1.4 Chapter 1 Summary and Review
Chapter 1 Review Problems
1.
Answer.
3.
Answer.
5.
Answer.
7.
Answer.
9.
Answer.
11.
Answer.
13.
Answer.
15.
Answer.
17.
Answer.
19.
Answer.
Yes, three pairs of equal angles
21.
Answer.
Yes, three pairs of equal angles
23.
Answer.
13
25.
Answer.
18
27.
Answer.
29.
Answer.
31.
Answer.
33.
Answer.
35.
Answer.
37.
Answer.
14 ft
39.
Answer.
41.
Answer.
All side have length opposite sides have slopes and
43.
Answer.
45.
Answer.
47.
Answer.
49.
Answer.
51.
Answer.
ft
53.
Answer.
Delbert in, in, Francine
2 The Trigonometric Ratios
2.1 Side and Angle Relationships
Homework 2.1
1.
Answer.
The sum of the angles is not
3.
Answer.
The exterior angle is not equal to the sum of the opposite interior angles.
5.
Answer.
The sum of the acute angles is not
7.
Answer.
The largest side is not opposite the largest angle.
9.
Answer.
The Pythagorean theorem is not satisfied.
11.
Answer.
13.
Answer.
15.
Answer.
17.
Answer.
21 in
19.
Answer.
21.
Answer.
The rectangle is inches by inches.
23.
Answer.
29
25.
Answer.
27.
Answer.
No
29.
Answer.
Yes
31.
Answer.
No
33.
Answer.
The distance from to is and the distance from to is also so the triangle is isosceles. The distance from to is 6, and so the triangle is a right triangle.
35.
Answer.
25 ft
37.
Answer.
39.
Answer.
41.
Answer.
- No
- Yes
43.
Answer.
and 2 and
2.2 Right Triangle Trigonometry
Homework 2.2
1.
Answer.
- 0.91
- 0.91
- 0.9063
3.
Answer.
- 0.77
- 0.77
- 0.7660
5.
Answer.
7.
Answer.
9.
Answer.
11.
Answer.
(Answers may vary)
13.
Answer.
(Answers may vary)
15.
Answer.
(Answers may vary)
17.
Answer.
14.41
19.
Answer.
37.86
21.
Answer.
86.08
23.
Answer.

25.
Answer.

27.
Answer.
170.1 yd
29.
Answer.
355.2 ft
31.
Answer.
1114.7 m
33.
Answer.
2284.2 m
35.
Answer.
37.
Answer.
39.
Answer.
41.
Answer.
43.
Answer.
45.
Answer.
47.
Answer.
49.
Answer.
51.
Answer.
and are complements. and The side opposite is the side adjacent to and vice versa.
53.
Answer.
- As
increases, increases also. The side opposite increases in length while the side adjacent to remains fixed. - As
increases, decreases. The side adjacent to remains fixed while the hypotenuse increases in length.
55.
Answer.
As decreases toward the side opposite approaches a length of 0, so sin approaches 0. But as increases toward the length of the side opposite approaches the length of the hypotenuse, so approaches 1.
57.
Answer.
The triangle is not a right tringle.
59.
Answer.
61.
Answer.
- 0.2358
- sine
63.
Answer.
65.
Answer.
Although the triangles may differ in size, the ratio of the side adjacent to the angle to the hypotenuse of the triangle remains the same because the triangles would all be similar, and hence corresponding sides are proportional.
67.
Answer.
2.3 Solving Right Triangles
Homework 2.3
1.
Answer.
3.
Answer.
5.
Answer.
7.
Answer.
9.
Answer.
11.
Answer.
- Solve
for - Solve
for - Subtract
from to find
13.
Answer.
- Solve
for - Solve
for - Subtract
from to find
15.
Answer.
- Solve
for - Solve
for - Subtract
from to find
17.
Answer.
19.
Answer.
21.
Answer.
23.
Answer.
25.
Answer.
27.
Answer.
29.
Answer.
31.
Answer.
33.
Answer.
35.
Answer.
37.
Answer.
39.
Answer.
41.
Answer.
43.
Answer.
cm
45.
Answer.
km
47.
Answer.
ft
49.
Answer.
(a) and (b)
51.
Answer.
(a) and (d)
53.
Answer.
55.
Answer.
57.
Answer.
59.
Answer.
undefined |
61.
Answer.
- smaller
- larger
- larger
63.
Answer.
65.
Answer.
67.
Answer.
69.
Answer.
71.
Answer.
73.
Answer.
cm sq cm
75.
Answer.
sq cm sq cm sq cm
77.
Answer.
sq in by area sq in
2.4 Chapter 2 Summary and Review
Chapter 2 Review Problems
1.
Answer.
If then
3.
Answer.
If then
5.
Answer.
If then
7.
Answer.
9.
Answer.
11.
Answer.
13.
Answer.
Yes
15.
Answer.
17.
Answer.
No. or
19.
Answer.
21.
Answer.
23.
Answer.
25.
Answer.
27.
Answer.
29.
Answer.
31.
Answer.
33.
Answer.
35.
Answer.
37.
Answer.
39.
Answer.
41.
Answer.
43.
Answer.
3 Laws of Sines and Cosines
3.1 Obtuse Angles
Homework 3.1
1.
Answer.
3.
Answer.
5.
Answer.
7.
Answer.
9.
Answer.
11.
Answer.
13.
Answer.
15.
Answer.
17.
Answer.
19.
Answer.
21.
Answer.
23.
Answer.
25.
Answer.
27.
Answer.
29.
Answer.
31.
Answer.
33.
Answer.
35.
Answer.
37.
Answer.
39.
Answer.
41.
Answer.
in, in sq in
43.
Answer.
mi, mi sq mi
45.
Answer.
47.
Answer.
49.
Answer.
51.
Answer.
55.
Answer.
57.
Answer.
59.
Answer.
61.
Answer.
63.
Answer.
Bob found an acute angle. The obtuse angle is the supplement of or
65.
Answer.
67.
Answer.
69.
Answer.
3.2 The Law of Sines
Homework 3.2
1.
Answer.
3.
Answer.
5.
Answer.
7.
Answer.
9.
Answer.
11.
Answer.
13.
Answer.
15.
Answer.
17.
Answer.
19.
Answer.
a.
b. 808.1 ft
21.
Answer.
a.
b. 68.2 km
23.
Answer.
a.
b.1.23 mi 0.99 mi; 0.22 mi
25.
Answer.
a.
b. 322.6 m
27.
Answer.
- 2617.2 ft
- 1022.6 ft
29.
Answer.
540,000 AU km
31.
Answer.
750,000 AU km
33.
Answer.
- No,
is too short. - 2
- 1
35.
Answer.
-
1,
-
0,
-
2,
-
1,
37.
Answer.
or- no solution
- 5.14
39.
Answer.
41.
Answer.
43.
Answer.
1299 yd or 277.2 yd
45.
Answer.
- 11.79
- 24.16
- 24.16
47.
Answer.

49.
Answer.
- ii
3.3 The Law of Cosines
Homework 3.3
1.
Answer.
- 12.78
- 135.22
3.
Answer.
5.
Answer.
7.
Answer.
7.70
9.
Answer.
13.44
11.
Answer.
5.12
13.
Answer.
15.
Answer.
17.
Answer.
19.
Answer.
21.
Answer.
6.30 or 2.70
23.
Answer.
29.76 or 5.91
25.
Answer.
16.00
27.
Answer.
Law of Cosines:
29.
Answer.
Law of Sines:
31.
Answer.
First the Law of Cosines: then either the Law of Sines: or the Law of Cosines:
33.
Answer.
Law of Cosines: or use the Law of Sines first to find the (acute) angle opposite the side of length 4, then find the angle opposite the side of length by subtracting the sum of the known angles from then using the Law of Sines again.
35.
Answer.
37.
Answer.
39.
Answer.
or
41.
Answer.
43.
Answer.
- 1383.3 m
45.
Answer.
- 2123 mi,
east of north
47.
Answer.
west of south, 917.9 mi
49.
Answer.
- 92.99 ft
51.
Answer.
53.
Answer.
10.53
55.
Answer.
4.08
57.
Answer.
- First figure:
is the base of the small right triangle. Second: is the horizontal distance between and the -axis, so or is the base of the large right triangle. Third: and is the base of a right triangle. - First:
and are the legs of a right triangle, is the hypotenuse. Second: and are the legs of a right triangle with hypotenuse Third: and
59.
Answer.
so and dividing both sides by yields
61.
Answer.
For the first equation, start with the Law of Cosines in the form
Add to both sides of the equation, factor the right side, then divide both sides by
For the second equation, start with the Law of Cosines in the form
Add to both sides of the equation, factor the right side, then divide both sides by
3.4 Chapter 3 Summary and Review
Chapter 3 Review Problems
1.
Answer.
3.
Answer.
- 49.33
-
5.
Answer.
7.
Answer.
9.
Answer.
11.
Answer.
13.
Answer.
15.
Answer.
17.
Answer.
19.
Answer.
5127.39 sq ft
21.
Answer.
23.
Answer.
25.
Answer.
27.
Answer.
29.
Answer.
31.
Answer.
- 8.82
33.
Answer.
35.
Answer.
- 16.29
37.
Answer.
39.
Answer.
- 17.40
or
- 80.93
41.
Answer.
- 16.08 mi, 80.4 mph
43.
Answer.
- 72.47
45.
Answer.
-
353.32
- 217.52 m
47.
Answer.
- 79.64 m
- 46.12 m
49.
Answer.
51.
Answer.
4.2
53.
Answer.
22.25 ft
55.
Answer.
79,332.6 AU
57.
Answer.
bisects the central angle at and the inscribed angle is half the central angle at
4 Trigonometric Functions
4.1 Angles and Rotation
Homework 4.1
1.
Answer.
3.
Answer.
5.
Answer.
7.
Answer.
9.
Answer.
11.
Answer.
13.
Answer.
15.
Answer.
17.
Answer.
19.
Answer.
21.
Answer.
23.
Answer.
25.
Answer.
27.
Answer.
29.
Answer.
31.
Answer.
33.
Answer.
35.
Answer.
37.
Answer.
39.
Answer.
41.
Answer.
43.
Answer.
45.
Answer.
47.
Answer.
49.
Answer.
51.
Answer.
53.
Answer.
55.
Answer.
- III and IV
- II and III
- I and III
57.
Answer.
59.
Answer.
61.
Answer.
63.
Answer.
65.
Answer.
Sides of similar triangles are proportional.
4.2 Graphs of Trigonometric Functions
Homework 4.2
1.
Answer.
3.
Answer.
5.
Answer.
7.
Answer.
9.
Answer.
11.
Answer.
13.
Answer.
15.
Answer.
17.
Answer.
19.
Answer.
21.
Answer.
23.
Answer.
- The calculator gives an error message because
is undefined.
25.
Answer.
27.
Answer.
29.
Answer.
31.
Answer.
33.
Answer.
35.
Answer.
37.
Answer.
39.
Answer.
41.
Answer.
43.
Answer.
amp period midline:
45.
Answer.
amp period midline:
47.
Answer.
amp period midline:
49.
Answer.
- amp
period midline:
51.
Answer.
- amp
period midline:
53.
Answer.
- amp
period midline:
55.
Answer.
- amp
period midline:
57.
Answer.
59.
Answer.
61.
Answer.
63.
Answer.
65.
Answer.
4.3 Using Trigonometric Functions
Homework 4.3
1.
Answer.
3.
Answer.
5.
Answer.
7.
Answer.
9.
Answer.
11.
Answer.
13.
Answer.
15.
Answer.
17.
Answer.
19.
Answer.
21.
Answer.
23.
Answer.
25.
Answer.
27.
Answer.
29.
Answer.
31.
Answer.
33.
Answer.
35.
Answer.
37.
Answer.
- 15.3 mi east, 21 mi north
39.
Answer.
- 91.9 km west, 77.1 km south
41.
Answer.
- 30.9 km west, 8.3 km north
43.
Answer.
45.
Answer.
47.
Answer.
49.
Answer.
51.
Answer.
not periodic
53.
Answer.
Periodic with period 4
55.
Answer.
- 10 minutes
57.
Answer.
- 1 week
59.
Answer.
- period 1 sec, midline
amp 10 inches
61.
Answer.
- period 1 year, midline
amp 2500
63.
Answer.
- period 1 year, midline
amp 21
65.
Answer.
a. IV b. III c. II d. I
67.
Answer.
69.
Answer.
- Emotional high: Oct 5 and Nov 3, low: Oct 19; Physical high: Sep 30 and Oct 23, low: Oct 12 and Nov 4; Intellectual high: Oct 10, low: Oct 26
- Emotional: 28 days, physical: 23 days, intellectual: 32 days
- 5152 days
71.
Answer.
- periodic, period 8
- 4, midline:
73.
Answer.
- systolic 120 mm Hg, diastolic 80 mm Hg, pulse pressure 40 mm Hg.
- 72 beats per minute
75.
Answer.
- 69 hours.
- 2.2 to 3.5
- The larger dip corresponds to when the brighter star is eclipsed, the smaller dip corresponds to when the dimmer star is eclipsed.
4.4 Chapter 4 Summary and Review
Chapter 4 Review Problems
1.
Answer.
3.
Answer.
5.
Answer.
7.
Answer.
9.
Answer.
11.
Answer.
13.
Answer.
15.
Answer.
17.
Answer.
19.
Answer.
21.
Answer.
23.
Answer.
25.
Answer.
27.
Answer.
29.
Answer.
31.
Answer.
33.
Answer.
south: 1.74 mi, west: 9.85 mi
35.
Answer.
37.
Answer.
39.
Answer.
41.
Answer.
0
43.
Answer.
45.
Answer.
47.
Answer.
- 24 hours
49.
Answer.
- 20 sec
51.
Answer.
- amp: 2, period:
midline:
53.
Answer.
- amp: 3.5, period:
midline:
55.
Answer.
57.
Answer.
59.
Answer.
61.
Answer.
63.
Answer.
The -intercepts of occur at the vertical asymptotes of
5 Equations and Identities
5.1 Algebra with Trigonometric Ratios
Homework 5.1
1.
Answer.
3.
Answer.
5.
Answer.
7.
Answer.
9.
Answer.
11.
Answer.
13.
Answer.
15.
Answer.
17.
Answer.
19.
Answer.
21.
Answer.
23.
Answer.
25.
Answer.
27.
Answer.
29.
Answer.
31.
Answer.
33.
Answer.
35.
Answer.
No
37.
Answer.
No
39.
Answer.
Yes
41.
Answer.
No
43.
Answer.
No
45.
Answer.
47.
Answer.
49.
Answer.
51.
Answer.
53.
Answer.
55.
Answer.
57.
Answer.
59.
Answer.
61.
Answer.
63.
Answer.
65.
Answer.
67.
Answer.
69.
Answer.
5.2 Solving Equations
Homework 5.2
1.
Answer.
3.
Answer.
5.
Answer.
I: II: III: IV:
7.
Answer.
I: II: III: IV:
9.
Answer.
11.
Answer.
13.
Answer.
15.
Answer.
17.
Answer.
19.
Answer.
21.
Answer.
23.
Answer.
25.
Answer.
27.
Answer.
29.
Answer.
31.
Answer.
33.
Answer.
35.
Answer.
37.
Answer.
39.
Answer.
41.
Answer.
43.
Answer.
45.
Answer.
47.
Answer.
49.
Answer.
51.
Answer.
53.
Answer.
55.
Answer.
57.
Answer.
59.
Answer.
61.
Answer.
63.
Answer.
65.
Answer.
67.
Answer.
5.3 Trigonometric Identities
Homework 5.3
1.
Answer.
not an identity
3.
Answer.
not an identity
5.
Answer.
identity
7.
Answer.
not an identity
9.
Answer.
not an identity
11.
Answer.
not an identity
13.
Answer.
identity
15.
Answer.
identity
17.
Answer.
19.
Answer.
21.
Answer.
23.
Answer.
25.
Answer.
27.
Answer.
29.
Answer.
31.
Answer.
33.
Answer.
35.
Answer.
37.
Answer.
39.
Answer.
41.
Answer.
43.
Answer.
45.
Answer.
47.
Answer.
49.
Answer.
51.
Answer.
53.
Answer.
55.
Answer.
57.
Answer.
59.
Answer.
61.
Answer.
63.
Answer.
65.
Answer.
67.
Answer.
69.
Answer.
71.
Answer.
73.
Answer.
75.
Answer.
77.
Answer.

- By the distance formula,
or
5.4 Chapter 5 Summary and Review
Chapter 5 Review Problems
1.
Answer.
3.
Answer.
5.
Answer.
No
7.
Answer.
Yes
9.
Answer.
11.
Answer.
13.
Answer.
Not equivalent
15.
Answer.
Equivalent
17.
Answer.
19.
Answer.
21.
Answer.
23.
Answer.
25.
Answer.
27.
Answer.
29.
Answer.
31.
Answer.
33.
Answer.
35.
Answer.
37.
Answer.
39.
Answer.
41.
Answer.
43.
Answer.
45.
Answer.
47.
Answer.
Identity
49.
Answer.
Not an identity
51.
Answer.
Not an identity
53.
Answer.
Identity
55.
Answer.
57.
Answer.
59.
Answer.
61.
Answer.
63.
Answer.
65.
Answer.
67.
Answer.
69.
Answer.
71.
Answer.
73.
Answer.
75.
Answer.
77.
Answer.
79.
Answer.
81.
Answer.
6 Radians
6.1 Arclength and Radians
Homework 6.1
1.
Answer.
Radians | |||||||||
Degrees |
3.
Answer.
5.
Answer.
7.
Answer.
9.
Answer.
11.
Answer.
13.
Answer.
15.
Answer.
17.
Answer.
19.
Answer.
21.
Answer.
- II
- IV
- IV
- I
23.
Answer.
- III
- II
- I
- IV
25.
Answer.
Radians | |||
Degrees |
27.
Answer.
Radians | |||
Degrees |
29.
Answer.
31.
Answer.
33.
Answer.
35.
Answer.
37.
Answer.
39.
Answer.
41.
Answer.
43.
Answer.
45.
Answer.
47.
Answer.
49.
Answer.
51.
Answer.
53.
Answer.
-
- Arclength doubles; arclength triples
55.
Answer.
57.
Answer.
59.
Answer.
6.2 The Circular Functions
Homework 6.2
1.
Answer.
a | b | c | d | |
3.
Answer.
a | b | c | d | |
5.
Answer.
7.
Answer.
9.
Answer.
11.
Answer.
13.
Answer.
15.
Answer.
II
17.
Answer.
II
19.
Answer.
III
21.
Answer.
Negative
23.
Answer.
Positive
25.
Answer.
Positive
27.
Answer.
29.
Answer.
31.
Answer.
January 1: 4:24, April 1: 6:45, July 1: 8:02, October 1: 5:55
33.
Answer.
35.
Answer.
37.
Answer.
39.
Answer.
41.
Answer.
43.
Answer.
45.
Answer.
47.
Answer.
49.
Answer.
51.
Answer.
53.
Answer.
55.
Answer.
57.
Answer.
59.
Answer.
61.
Answer.
63.
Answer.
65.
Answer.
67.
Answer.
-
Intersections:
and and
69.
Answer.
71.
Answer.
73.
Answer.
75.
Answer.
Any point on the terminal side of satisfies For the point where The arc of length is spanned by an angle in standard position. Because arclength is and so
77.
Answer.
The two right triangles shown are similar, so their sides are proportional. The hypotenuse of the large triangle is times the hypotenuse of the small triangle, so the two legs of the large triangle must be times the legs of the small triangle. Thus, because the coordinates of the vertex on the unit circle are the coordinates of must be
79.
Answer.
71 m west, 587 m north
6.3 Graphs of the Circular Functions
Homework 6.3
1.
Answer.
3.
Answer.
5.
Answer.
- Domain:
range:
7.
Answer.
- Domain:
an odd integer, range:
9.
Answer.
or or
11.
Answer.
or or
13.
Answer.
15.
Answer.
17.
Answer.
19.
Answer.
21.
Answer.
I: 0.5, II: 2.7, III: 3.6, IV: 5.8
23.
Answer.
I: 0.6, II: 2.6, III: 3.7, IV: 5.7
25.
Answer.
I: 1.3, II: 1.8, III: 4.5, IV: 4.9
27.
Answer.
29.
Answer.
31.
Answer.
33.
Answer.
35.
Answer.
37.
Answer.
39.
Answer.
41.
Answer.
43.
Answer.
45.
Answer.
47.
Answer.
49.
Answer.
- No solution
51.
Answer.
53.
Answer.
55.
Answer.
57.
Answer.
59.
Answer.
b-c.
d. and e. to
61.
Answer.
b-c.
d. High: day 204, low: day 25, e. to
63.
Answer.
65.
Answer.
67.
Answer.
69.
Answer.
71.
Answer.
- Domain:
range:
73.
Answer.
- Domain:
range:
75.
Answer.
- Domain:
range:
77.
Answer.
- Domain:
range:
79.
Answer.
-
- Domain:
Range:
6.4 Chapter 6 Summary and Review
Chapter 6 Review Problems
1.
Answer.
3.
Answer.
5.
Answer.
7.
Answer.
9.
Answer.
11.
Answer.
13.
Answer.
- II
- I
- IV
15.
Answer.
17.
Answer.
19.
Answer.
21.
Answer.
23.
Answer.
25.
Answer.
27.
Answer.
29.
Answer.
31.
Answer.
33.
Answer.
35.
Answer.
37.
Answer.
39.
Answer.
41.
Answer.
43.
Answer.
- mid:
amp: period:
45.
Answer.
- mid:
amp: period:
47.
Answer.
49.
Answer.
51.
Answer.
53.
Answer.
55.
Answer.
57.
Answer.
59.
Answer.
61.
Answer.
63.
Answer.
Dom: all real numbers, Rge:
65.
Answer.
Dom: Rge:
67.
Answer.
- Yes
7 Circular Functions
7.1 Transformations of Graphs
Homework 7-1
1.
Answer.
amplitude period midline
3.
Answer.
amplitude period midline
5.
Answer.
amplitude period midline
7.
Answer.
amplitude period midline
9.
Answer.
11.
Answer.
13.
Answer.
15.
Answer.
17.
Answer.
19.
Answer.
21.
Answer.
23.
Answer.
- amplitude
period midline
25.
Answer.
- amplitude
period midline
27.
Answer.
- amplitude
period midline
29.
Answer.
- amplitude
period midline
31.
Answer.
33.
Answer.
35.
Answer.
37.
Answer.
39.
Answer.
41.
Answer.
43.
Answer.
45.
Answer.
47.
Answer.
49.
Answer.
51.
Answer.
53.
Answer.
-
undef undef - period
midline
55.
Answer.
-
undef undef - period
midline
57.
Answer.
-
undef undef - period
midline
59.
Answer.
61.
Answer.
63.
Answer.
65.
Answer.
67.
Answer.
69.
Answer.
7.2 The General Sinusoidal Function
Homework 7-2
1.
Answer.
to the right
3.
Answer.
undef undef undef undef to the left
5.
Answer.
- amplitude 2, shift
to the left
7.
Answer.
9.
Answer.
11.
Answer.
- period
shift to the right
13.
Answer.
- period 2, shift
to the left
15.
Answer.
- midline
period horizontal shift to the right, amplitude 3 - no solution for
17.
Answer.
19.
Answer.
21.
Answer.
23.
Answer.
25.
Answer.
27.
Answer.
- midline
period 12, amplitude 36.95
29.
Answer.
- midline
period amplitude 1.4 - high 11:10 am, low 5:19 pm
31.
Answer.
- amplitude 3.2, period 2, midline
33.
Answer.
- amplitude 5, period 1, midline
7.3 Solving Equations
Homework 7-3
1.
Answer.
3.
Answer.
5.
Answer.
7.
Answer.
9.
Answer.
11.
Answer.
13.
Answer.
15.
Answer.
17.
Answer.
19.
Answer.
21.
Answer.
23.
Answer.
25.
Answer.
27.
Answer.
29.
Answer.
31.
Answer.
33.
Answer.
35.
Answer.
37.
Answer.
39.
Answer.
41.
Answer.
43.
Answer.
months (Dec) or months (June) is less than 45,000 between and
45.
Answer.
sec or sec- Delbert is above 18 m between
and
7.4 Chapter 7 Summary and Review
Review Problems
1.
Answer.
amp: period: mid:
3.
Answer.
amp: period: mid:
5.
Answer.
7.
Answer.
9.
Answer.
11.
Answer.
13.
Answer.
- period:
shift: left
15.
Answer.
- mid:
period: 0, amp: 5 -
Fill in the table of values.
- 30
- 15, 45
17.
Answer.
19.
Answer.
- 0.57, 3.07, 3.71
21.
Answer.
23.
Answer.
- amp: 3, period: 12, midline:
25.
Answer.
27.
Answer.
29.
Answer.
0.066, 1.113, 2.160, 3.207, 4.255, 5.302
31.
Answer.
1.150, 1.991, 4.292, 5.133
33.
Answer.
35.
Answer.
No solution
37.
Answer.
0.375, 1.422, 2.470, 3.517, 4.564, 5.611
39.
Answer.
2.120, 4.880
8 More Functions and Identities
8.1 Sum and Difference Formulas
Homework 8-1
1.
Answer.
3.
Answer.
5.
Answer.
7.
Answer.
9.
Answer.
11.
Answer.
The curves are different.
13.
Answer.
15.
Answer.
17.
Answer.
19.
Answer.
21.
Answer.
23.
Answer.
25.
Answer.
27.
Answer.
29.
Answer.
31.
Answer.
No
33.
Answer.
No
35.
Answer.
37.
Answer.
39.
Answer.
False, but
41.
Answer.
False, but
43.
Answer.
45.
Answer.
47.
Answer.
49.
Answer.
51.
Answer.
53.
Answer.
55.
Answer.
57.
Answer.
59.
Answer.
61.
Answer.
63.
Answer.
65.
Answer.
67.
Answer.
,
69.
Answer.
71.
Answer.
, ,
73.
Answer.
75.
Answer.
77.
Answer.
79.
Answer.
- Not an identity.
(many answers possible)
81.
Answer.
Identity
83.
Answer.
- Not an identity.
(many answers possible)
85.
Answer.
Identity
87.
Answer.
Identity
89.
Answer.
and are both complements of and are alternate interior angles
91.
Answer.
8.2 Inverse Trigonometric Functions
Homework 8-2
1.
Answer.
No inverse: Some horizontal lines intersect the curve in more than one point.
3.
Answer.
Inverse exists: The function is 1-1.
5.
Answer.
No inverse
7.
Answer.
No inverse
9.
Answer.
11.
Answer.
13.
Answer.
15.
Answer.
17.
Answer.
19.
Answer.
21.
Answer.
so the angle of elevation is when the rocket is 1000 yd high.
23.
Answer.
the bilboard subtends an angle of at a distance of 200 ft.
25.
Answer.
so the painting subtends an angle of when Martin is 5 meters from the wall.
27.
Answer.
29.
Answer.
31.
Answer.
33.
Answer.
35.
Answer.
37.
Answer.
39.
Answer.
41.
Answer.
43.
Answer.
45.
Answer.
47.
Answer.
49.
Answer.
a–b.
c. No
51.
Answer.
a.
c. No
53.
Answer.
55.
Answer.
57.
Answer.
59.
Answer.
61.
Answer.
63.
Answer.
65.
Answer.
67.
Answer.
69.
Answer.
- Yes.
- All
or
71.
Answer.
- Domain:
range: - Let
Then and So .
73.
Answer.
8.3 The Reciprocal Functions
Homework 8-3
1.
Answer.
3.
Answer.
5.
Answer.
7.
Answer.
9.
Answer.
11.
Answer.
13.
Answer.
15.
Answer.
17.
Answer.
undefined | |||||||||
undefined | undefined | ||||||||
undefined | undefined |
19.
Answer.
21.
Answer.
23.
Answer.
25.
Answer.
27.
Answer.
29.
Answer.
- 155.572 miles
31.
Answer.
- 0.78 sec
33.
Answer.
35.
Answer.
37.
Answer.
39.
Answer.
41.
Answer.
43.
Answer.
45.
Answer.
47.
Answer.
49.
Answer.
51.
Answer.
53.
Answer.
undefined | undefined |
55.
Answer.
57.
Answer.
undefined | undefined | undefined |
59.
Answer.
61.
Answer.
63.
Answer.
65.
Answer.
67.
Answer.
69.
Answer.
71.
Answer.
73.
Answer.
75.
Answer.
77.
Answer.
79.
Answer.
81.
Answer.
83.
Answer.
85.
Answer.
87.
Answer.
89.
Answer.
91.
Answer.
93.
Answer.
95.
Answer.
8.4 Chapter Summary and Review
Review Problems
1.
Answer.
False
3.
Answer.
True
5.
Answer.
False
7.
Answer.
False
9.
Answer.
11.
Answer.
13.
Answer.
15.
Answer.
17.
Answer.
19.
Answer.
21.
Answer.
23.
Answer.
25.
Answer.
27.
Answer.

No
29.
Answer.
31.
Answer.
33.
Answer.
35.
Answer.
37.
Answer.
39.
Answer.
Because is undefined for If then either or If then is undefined.
41.
Answer.
43.
Answer.
45.
Answer.
47.
Answer.
49.
Answer.
51.
Answer.
53.
Answer.
55.
Answer.
57.
Answer.
59.
Answer.
61.
Answer.
63.
Answer.
65.
Answer.
67.
Answer.
69.
Answer.
71.
Answer.
73.
Answer.
75.
Answer.
77.
Answer.
79.
Answer.
81.
Answer.
83.
Answer.
- They are right triangles that share
is the complement of and is the complement of so- They are right triangles with
so and are ratios of corresponding sides of similar triangles; by part (a), by part (d).
85.
Answer.
9 Vectors
9.1 Geometric Form
Homework 9-1
1.
Answer.
3.
Answer.
5.
Answer.
7.
Answer.
9.
Answer.
11.
Answer.
13.
Answer.
15.
Answer.
17.
Answer.
19.
Answer.
21.
Answer.
23.
Answer.
25.
Answer.
27.
Answer.
29.
Answer.
31.
Answer.
33.
Answer.
35.
Answer.
4.47 mi, east of north
37.
Answer.
129.4 mph, west of north
39.
Answer.
- 19.9 mph,
east of north
41.
Answer.
- 1.9 km,
west of north
43.
Answer.
45.
Answer.
47.
Answer.
49.
Answer.
51.
Answer.
9.2 Coordinate Form
Homework 9-2
1.
Answer.
3.
Answer.
5.
Answer.
and
7.
Answer.
9.
Answer.
11.
Answer.
13.
Answer.
15.
Answer.
17.
Answer.
19.
Answer.
21.
Answer.
23.
Answer.
25.
Answer.
27.
Answer.
29.
Answer.
31.
Answer.
33.
Answer.
35.
Answer.
37.
Answer.
39.
Answer.
41.
Answer.
43.
Answer.
45.
Answer.
47.
Answer.
49.
Answer.
51.
Answer.
- 1700 m,
east of south
53.
Answer.
- 21.98 km,
north of west
55.
Answer.
- 83 mi,
east of north
57.
Answer.
59.
Answer.
61.
Answer.
9.3 The Dot Product
Homework 9-3
1.
Answer.
3.
Answer.
5.
Answer.
7.
Answer.
9.
Answer.
11.
Answer.
13.
Answer.
15.
Answer.
17.
Answer.
19.
Answer.
not orthogonal
21.
Answer.
orthogonal
23.
Answer.
25.
Answer.
27.
Answer.
29.
Answer.
31.
Answer.
33.
Answer.
35.
Answer.
37.
Answer.
38.57 lbs
39.
Answer.
1289 lbs
41.
Answer.
and
43.
Answer.
45.
Answer.
47.
Answer.
49.
Answer.
51.
Answer.
- Both
and because
53.
Answer.
- Let
and
9.4 Chapter Summary and Review
Review Problems
1.
Answer.
3.
Answer.
5.
Answer.
7.
Answer.
9.
Answer.
11.
Answer.
13.
Answer.
15.
Answer.
17.
Answer.
19.
Answer.
21.
Answer.
23.
Answer.
25.
Answer.
27.
Answer.
29.
Answer.
31.
Answer.
10 Polar Coordinates and Complex Numbers
10.1 Polar Coordinates
Homework 10-1
1.
Answer.
3.
Answer.
5.
Answer.
7.
Answer.
9.
Answer.
11.
Answer.
13.
Answer.
15.
Answer.
17.
Answer.
19.
Answer.
21.
Answer.
23.
Answer.
25.
Answer.
27.
Answer.
29.
Answer.
31.
Answer.
33.
Answer.
35.
Answer.
37.
Answer.
39.
Answer.
41.
Answer.
43.
Answer.
45.
Answer.
47.
Answer.
49.
Answer.
51.
Answer.
53.
Answer.
55.
Answer.
57.
Answer.
59.
Answer.
61.
Answer.
63.
Answer.
65.
Answer.
67.
Answer.
69.
Answer.
71.
Answer.
73.
Answer.
10.2 Polar Graphs
Homework 10-2
1.
Answer.
-
is the radius
3.
Answer.
-
is the slope
5.
Answer.
The graph of begins at the right-most point (and proceeds counter-clockwise); the graph of begins at the left-most point.
7.
Answer.
-
The graph is traced again.
- center:
radius:
9.
Answer.
- For
is the radius of a circle centerd on the positive -axis; for is the radius of a circle centerd on the negative -axis.
11.
Answer.
13.
Answer.
15.
Answer.
-
There are
petals if is odd, and petals if is even. -
is the length of the petal.
17.
Answer.
is the length of the loop.
19.
Answer.
21.
Answer.
23.
Answer.
25.
Answer.
circle
27.
Answer.
line
29.
Answer.
circle
31.
Answer.
cardioid
33.
Answer.
limaçon
35.
Answer.
rose
37.
Answer.
rose
39.
Answer.
limaçon
41.
Answer.
lemniscate
43.
Answer.
circle
45.
Answer.
arcs of a circle
47.
Answer.
semicircle
49.
Answer.
rose
51.
Answer.
cardioid
53.
Answer.
parabola
55.
Answer.
ellipse
57.
Answer.
hyperbola
59.
Answer.
61.
Answer.
63.
Answer.
65.
Answer.
67.
Answer.
69.
Answer.
71.
Answer.
73.
Answer.
75.
Answer.
77.
Answer.
79.
Answer.
81.
Answer.
83.
Answer.
The curve has large loops and small loops.
10.3 Complex Numbers
Homework 10-3
1.
Answer.
3.
Answer.
5.
Answer.
7.
Answer.
9.
Answer.
11.
Answer.
13.
Answer.
15.
Answer.
17.
Answer.
19.
Answer.
21.
Answer.
23.
Answer.
25.
Answer.
27.
Answer.
29.
Answer.
31.
Answer.
33.
Answer.
35.
Answer.
37.
Answer.
39.
Answer.
41.
Answer.
43.
Answer.
45.
Answer.
47.
Answer.
49.
Answer.
51.
Answer.
53.
Answer.
55.
Answer.
57.
Answer.
59.
Answer.
61.
Answer.
63.
Answer.
65.
Answer.
No. Let and Then so but
67.
Answer.
69.
Answer.
71.
Answer.
73.
Answer.
10.4 Polar Form for Complex Numbers
Homework 10-4
1.
Answer.
3.
Answer.
5.
Answer.
7.
Answer.
9.
Answer.
11.
Answer.
13.
Answer.
15.
Answer.
17.
Answer.
19.
Answer.
21.
Answer.
23.
Answer.
If then
25.
Answer.
27.
Answer.
29.
Answer.
31.
Answer.
33.
Answer.
35.
Answer.
37.
Answer.
39.
Answer.
41.
Answer.
43.
Answer.
45.
Answer.
,
47.
Answer.
49.
Answer.
51.
Answer.
53.
Answer.
55.
Answer.
57.
Answer.
59.
Answer.
61.
Answer.
63.
Answer.
65.
Answer.
10.5 Chapter Summary and Review
Review Problems
1.
Answer.
3.
Answer.
5.
Answer.
7.
Answer.
9.
Answer.
11.
Answer.
13.
Answer.
15.
Answer.
17.
Answer.
19.
Answer.
21.
Answer.
23.
Answer.
25.
Answer.
Circle of radius 3 centered at the origin
27.
Answer.
Circle of radius 3 centered at