Solution manual for trigonometry 5th edition
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Solution Manual for Trigonometry, 5th Edition by Cynthia Y. Young
CHAPTER 1
Section 1.1 Solutions --------------------------------------------------------------------------------
1 x 1 x
1. Solve for x: 2. Solve for x:
2 360∘ 4 360∘
360∘ 2x, so that x 180∘ . 360∘ 4x, so that x 90∘ .
1 x 2 x
3. Solve for x: 4. Solve for x:
3 360∘ 3 360∘
360∘ 3x, so that x 120∘ . 720∘ 2(360∘ ) 3x, so that x 240∘ .
(Note: The angle has a negative (Note: The angle has a negative
measure since it is a clockwise measure since it is a clockwise rotation.)
rotation.)
5 x 7 x
5. Solve for x: 6. Solve for x:
6 360∘ 12 360∘
1800∘ 5(360∘ ) 6x, so that x 300∘ . 2520∘ 7(360∘ ) 12x, so that x 210∘ .
4 x 5 x
7. Solve for x: 8. Solve for x:
5 360∘ 9 360∘
1440∘ 4(360∘ ) 5x, so that 1800∘ 5(360∘ ) 9x, so that
x 288∘ . x 200∘ .
(Note: The angle has a negative (Note: The angle has a negative
measure since it is a clockwise measure since it is a clockwise rotation.)
rotation.)
9. 10.
a) complement: 90∘ 18∘ 72∘ a) complement: 90∘ 39∘ 51∘
b) supplement: 180∘ 18∘ 162∘ b) supplement: 180∘ 39∘ 141∘
11. 12.
a) complement: 90∘ 42∘ 48∘ a) complement: 90∘ 57∘ 33∘
b) supplement: 180∘ 42∘ 138∘ b) supplement: 180∘ 57∘ 123∘
1
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Solution
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Chapter 1
13. 14.
a) complement: 90∘ 89∘ 1∘ a) complement: 90∘ 75∘ 15∘
b) supplement: 180∘ 89∘ 91∘ b) supplement: 180∘ 75∘ 105∘
15. Since the angles with measures 4x ∘ and 6x ∘ are assumed to be
complementary, we know that 4x ∘ 6x ∘ 90∘. Simplifying this yields
10x ∘ 90∘ , so that x 9. So, the two angles have measures 36∘ and 54∘ .
16. Since the angles with measures 3x ∘ and 15x ∘ are assumed to be
supplementary, we know that 3x ∘ 15x ∘ 180∘. Simplifying this yields
18x ∘ 180∘ , so that x 10. So, the two angles have measures 30∘ and 150∘ .
17. Since the angles with measures 8x ∘ and 4x ∘ are assumed to be
supplementary, we know that 8x ∘ 4x ∘ 180∘. Simplifying this yields
12x ∘ 180∘ , so that x 15. So, the two angles have measures 60∘ and 120∘ .
18. Since the angles with measures 3x 15 ∘ and 10x 10 ∘ are assumed to be
complementary, we know that 3x 15 ∘ 10x 10 ∘ 90∘. Simplifying this yields
13x 25 ∘ 90∘ , so that 13x ∘ 65∘ and thus, x 5. So, the two angles have
measures 30∘ and 60∘ .
19. Since 180∘ , we know 20. Since 180∘ , we know
that that
117∘ 33∘ 180∘ and so, 30∘ . 110∘ 45 ∘ 180∘ and so, 25∘ .
– – – –
150∘ 155∘
21. Since 180∘ , we know 22. Since 180∘ , we know
that that
4 180∘ and so, 30∘. 3 180∘ and so, 36∘.
–– –– –– ––
6 5
Thus, 4 120∘ and 30∘ . Thus, 3 108∘ and 36∘ .
2
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Section 1.1
23. 180 ∘ 53.3∘ 23.6 ∘ 103.1∘ 24. 180 ∘ 105.6 ∘ 13.2∘ 61.2 ∘
25. Since this is a right triangle, we know from the Pythagorean Theorem that
a2 b2 c2. Using the given information, this becomes 42 32 c2 , which
simplifies to c2 25, so we conclude that c 5.
26. Since this is a right triangle, we know from the Pythagorean Theorem that
a2 b2 c2. Using the given information, this becomes 32 32 c2 , which
simplifies to c2 18, so we conclude that c 18 3 2 .
27. Since this is a right triangle, we know from the Pythagorean Theorem that
a2 b2 c2. Using the given information, this becomes 62 b2 102 , which
simplifies to 36 b2 100 and then to, b2 64, so we conclude that b 8.
28. Since this is a right triangle, we know from the Pythagorean Theorem that
a2 b2 c2. Using the given information, this becomes a2 72 122 , which
simplifies to a2 95, so we conclude that a 95 .
29. Since this is a right triangle, we know from the Pythagorean Theorem that
a2 b2 c2. Using the given information, this becomes 82 52 c2 , which
simplifies to c2 89, so we conclude that c 89 .
30. Since this is a right triangle, we know from the Pythagorean Theorem that
a2 b2 c2. Using the given information, this becomes 62 52 c2 , which
simplifies to c2 61, so we conclude that c 61 .
31. Since this is a right triangle, we know from the Pythagorean Theorem that
a2 b2 c2. Using the given information, this becomes 72 b2 112 , which
simplifies to b2 72, so we conclude that b 72 6 2 .
32. Since this is a right triangle, we know from the Pythagorean Theorem that
a2 b2 c2. Using the given information, this becomes a2 52 92 , which
simplifies to a2 56, so we conclude that a 56 2 14 .
3
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Solution
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Chapter 1
33. Since this is a right triangle, we know from the Pythagorean Theorem that
7
2
a 2 b 2 c 2 . Using the given information, this becomes a 2 5 2 , which
simplifies to a2 18, so we conclude that a 18 3 2 .
34. Since this is a right triangle, we know from the Pythagorean Theorem that
a2 b2 c2. Using the given information, this becomes 52 b2 102 , which
simplifies to b2 75, so we conclude that b 75 5 3 .
35. If x 10 in., then the hypotenuse 36. If x 8 m, then the hypotenuse of
of this triangle has length
this triangle has length 8 2 11.31 m .
10 2 14.14 in.
37. Let x be the length of a leg in the given 45∘ 45∘ 90∘ triangle. If the
hypotenuse of this triangle has length 2 2 cm, then 2 x 2 2, so that x 2.
Hence, the length of each of the two legs is 2 cm .
38. Let x be the length of a leg in the given 45∘ 45∘ 90∘ triangle. If the hypotenuse
10 10
of this triangle has length 10 ft., then 2 x 10, so that x 5.
2 2
Hence, the length of each of the two legs is 5 ft.
39. The hypotenuse has length 40. Since 2x 6m x 6 2
3 2m,
2
2 4 2 in. 8 in. each leg has length 3 2 m.
41. Since the lengths of the two legs of the given 30∘ 60∘ 90∘ triangle are x and
3 x, the shorter leg must have length x. Hence, using the given information, we
know that x 5 m. Thus, the two legs have lengths 5 m and 5 3 8.66 m, and
the hypotenuse has length 10 m.
42. Since the lengths of the two legs of the given 30∘ 60∘ 90∘ triangle are x and
3 x, the shorter leg must have length x. Hence, using the given information, we
know that x 9 ft. Thus, the two legs have lengths 9 ft. and 9 3 15.59 ft., and
the hypotenuse has length 18 ft.
4
Page 4 Solution manual for trigonometry 5th edition
Solution
by cynthia
manualyfor
young.pdf
trigonometry 5th edition by cynthia y young.pdf
Solution
by cynthia
manual
y young.pdf
for trigonometry 5th edition by cynthia y young Page 1 of 954
Solution Manual for Trigonometry, 5th Edition by Cynthia Y. Young
CHAPTER 1
Section 1.1 Solutions --------------------------------------------------------------------------------
1 x 1 x
1. Solve for x: 2. Solve for x:
2 360∘ 4 360∘
360∘ 2x, so that x 180∘ . 360∘ 4x, so that x 90∘ .
1 x 2 x
3. Solve for x: 4. Solve for x:
3 360∘ 3 360∘
360∘ 3x, so that x 120∘ . 720∘ 2(360∘ ) 3x, so that x 240∘ .
(Note: The angle has a negative (Note: The angle has a negative
measure since it is a clockwise measure since it is a clockwise rotation.)
rotation.)
5 x 7 x
5. Solve for x: 6. Solve for x:
6 360∘ 12 360∘
1800∘ 5(360∘ ) 6x, so that x 300∘ . 2520∘ 7(360∘ ) 12x, so that x 210∘ .
4 x 5 x
7. Solve for x: 8. Solve for x:
5 360∘ 9 360∘
1440∘ 4(360∘ ) 5x, so that 1800∘ 5(360∘ ) 9x, so that
x 288∘ . x 200∘ .
(Note: The angle has a negative (Note: The angle has a negative
measure since it is a clockwise measure since it is a clockwise rotation.)
rotation.)
9. 10.
a) complement: 90∘ 18∘ 72∘ a) complement: 90∘ 39∘ 51∘
b) supplement: 180∘ 18∘ 162∘ b) supplement: 180∘ 39∘ 141∘
11. 12.
a) complement: 90∘ 42∘ 48∘ a) complement: 90∘ 57∘ 33∘
b) supplement: 180∘ 42∘ 138∘ b) supplement: 180∘ 57∘ 123∘
1
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Solution
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Chapter 1
13. 14.
a) complement: 90∘ 89∘ 1∘ a) complement: 90∘ 75∘ 15∘
b) supplement: 180∘ 89∘ 91∘ b) supplement: 180∘ 75∘ 105∘
15. Since the angles with measures 4x ∘ and 6x ∘ are assumed to be
complementary, we know that 4x ∘ 6x ∘ 90∘. Simplifying this yields
10x ∘ 90∘ , so that x 9. So, the two angles have measures 36∘ and 54∘ .
16. Since the angles with measures 3x ∘ and 15x ∘ are assumed to be
supplementary, we know that 3x ∘ 15x ∘ 180∘. Simplifying this yields
18x ∘ 180∘ , so that x 10. So, the two angles have measures 30∘ and 150∘ .
17. Since the angles with measures 8x ∘ and 4x ∘ are assumed to be
supplementary, we know that 8x ∘ 4x ∘ 180∘. Simplifying this yields
12x ∘ 180∘ , so that x 15. So, the two angles have measures 60∘ and 120∘ .
18. Since the angles with measures 3x 15 ∘ and 10x 10 ∘ are assumed to be
complementary, we know that 3x 15 ∘ 10x 10 ∘ 90∘. Simplifying this yields
13x 25 ∘ 90∘ , so that 13x ∘ 65∘ and thus, x 5. So, the two angles have
measures 30∘ and 60∘ .
19. Since 180∘ , we know 20. Since 180∘ , we know
that that
117∘ 33∘ 180∘ and so, 30∘ . 110∘ 45 ∘ 180∘ and so, 25∘ .
– – – –
150∘ 155∘
21. Since 180∘ , we know 22. Since 180∘ , we know
that that
4 180∘ and so, 30∘. 3 180∘ and so, 36∘.
–– –– –– ––
6 5
Thus, 4 120∘ and 30∘ . Thus, 3 108∘ and 36∘ .
2
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Solution
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trigonometry 5th edition by cynthia y young.pdf
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Solution
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Section 1.1
23. 180 ∘ 53.3∘ 23.6 ∘ 103.1∘ 24. 180 ∘ 105.6 ∘ 13.2∘ 61.2 ∘
25. Since this is a right triangle, we know from the Pythagorean Theorem that
a2 b2 c2. Using the given information, this becomes 42 32 c2 , which
simplifies to c2 25, so we conclude that c 5.
26. Since this is a right triangle, we know from the Pythagorean Theorem that
a2 b2 c2. Using the given information, this becomes 32 32 c2 , which
simplifies to c2 18, so we conclude that c 18 3 2 .
27. Since this is a right triangle, we know from the Pythagorean Theorem that
a2 b2 c2. Using the given information, this becomes 62 b2 102 , which
simplifies to 36 b2 100 and then to, b2 64, so we conclude that b 8.
28. Since this is a right triangle, we know from the Pythagorean Theorem that
a2 b2 c2. Using the given information, this becomes a2 72 122 , which
simplifies to a2 95, so we conclude that a 95 .
29. Since this is a right triangle, we know from the Pythagorean Theorem that
a2 b2 c2. Using the given information, this becomes 82 52 c2 , which
simplifies to c2 89, so we conclude that c 89 .
30. Since this is a right triangle, we know from the Pythagorean Theorem that
a2 b2 c2. Using the given information, this becomes 62 52 c2 , which
simplifies to c2 61, so we conclude that c 61 .
31. Since this is a right triangle, we know from the Pythagorean Theorem that
a2 b2 c2. Using the given information, this becomes 72 b2 112 , which
simplifies to b2 72, so we conclude that b 72 6 2 .
32. Since this is a right triangle, we know from the Pythagorean Theorem that
a2 b2 c2. Using the given information, this becomes a2 52 92 , which
simplifies to a2 56, so we conclude that a 56 2 14 .
3
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Solution
by cynthia
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young.pdf
trigonometry 5th edition by cynthia y young.pdf
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Solution
by cynthia
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Chapter 1
33. Since this is a right triangle, we know from the Pythagorean Theorem that
7
2
a 2 b 2 c 2 . Using the given information, this becomes a 2 5 2 , which
simplifies to a2 18, so we conclude that a 18 3 2 .
34. Since this is a right triangle, we know from the Pythagorean Theorem that
a2 b2 c2. Using the given information, this becomes 52 b2 102 , which
simplifies to b2 75, so we conclude that b 75 5 3 .
35. If x 10 in., then the hypotenuse 36. If x 8 m, then the hypotenuse of
of this triangle has length
this triangle has length 8 2 11.31 m .
10 2 14.14 in.
37. Let x be the length of a leg in the given 45∘ 45∘ 90∘ triangle. If the
hypotenuse of this triangle has length 2 2 cm, then 2 x 2 2, so that x 2.
Hence, the length of each of the two legs is 2 cm .
38. Let x be the length of a leg in the given 45∘ 45∘ 90∘ triangle. If the hypotenuse
10 10
of this triangle has length 10 ft., then 2 x 10, so that x 5.
2 2
Hence, the length of each of the two legs is 5 ft.
39. The hypotenuse has length 40. Since 2x 6m x 6 2
3 2m,
2
2 4 2 in. 8 in. each leg has length 3 2 m.
41. Since the lengths of the two legs of the given 30∘ 60∘ 90∘ triangle are x and
3 x, the shorter leg must have length x. Hence, using the given information, we
know that x 5 m. Thus, the two legs have lengths 5 m and 5 3 8.66 m, and
the hypotenuse has length 10 m.
42. Since the lengths of the two legs of the given 30∘ 60∘ 90∘ triangle are x and
3 x, the shorter leg must have length x. Hence, using the given information, we
know that x 9 ft. Thus, the two legs have lengths 9 ft. and 9 3 15.59 ft., and
the hypotenuse has length 18 ft.
4
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Solution
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trigonometry 5th edition by cynthia y young.pdf
