Complete Solutions Manual — Trigonometry, 5th Edition — Cynthia Y. Young, 2021 — ISBN 9781119742623 — Latest Update 2025/2026 (All Chapters Covered 1–8)

Trigonometry – 5th Edition
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SOLUTIONS
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MANUAL
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Cynthia Y. Young
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Complete Solutions Manual for Instructors and
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Students
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© Cynthia Y. Young


All rights reserved. Reproduction or distribution without permission is prohibited.
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, Solution Manual for Trigonometry, 5th Edition by Cynthia Y. Young
CHAPTER 1
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Section 1.1 Solutions --------------------------------------------------------------------------------
1 x 1 x
1. Solve for x:  2. Solve for x: 
2 360∘ 4 360∘
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360∘  2x, so that x  180∘ . 360∘  4x, so that x  90∘ .

1 x 2 x
3. Solve for x:   4. Solve for x:  
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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
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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∘
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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∘
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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.)
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9. 10.
a) complement: 90∘ 18∘  72∘ a) complement: 90∘  39∘  51∘
b) supplement: 180∘ 18∘  162∘ b) supplement: 180∘  39∘  141∘
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11. 12.
a) complement: 90∘  42∘  48∘ a) complement: 90∘  57∘  33∘
b) supplement: 180∘  42∘  138∘ b) supplement: 180∘  57∘  123∘
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13. 14.
a) complement: 90∘  89∘  1∘ a) complement: 90∘  75∘  15∘
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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
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10x ∘  90∘ , so that x  9. So, the two angles have measures 36∘ and 54∘ .
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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∘ .
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17. Since the angles with measures 8x ∘ and  4x ∘ are assumed to be
supplementary, we know that  8x ∘   4x ∘  180∘. Simplifying this yields
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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
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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
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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
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that that
 4          180∘ and so,   30∘. 3         180∘ and so,   36∘.
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 6   5

Thus,   4   120∘ and     30∘ . Thus,   3  108∘ and     36∘ .
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23.   180 ∘  53.3∘  23.6 ∘   103.1∘ 24.   180 ∘  105.6 ∘ 13.2∘   61.2 ∘
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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
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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 .
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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
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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 
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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 
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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 .
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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 .
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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 .
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