Solution Manual for Trigonometry, 5th Edition by Cynthia Y. Young. Fully Solved trigonometry solutions.

Solution Manual
Trigonometry, 5th Edition
by Cynthia Y. Young




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, 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




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measure since it is a clockwise measure since it is a clockwise rotation.)
rotation.)

5. Solve for x:
5
6

360∘
x LE 6. Solve for x:
7
12

x
360∘
1800∘  5(360∘ )  6x, so that x  300∘ . 2520∘  7(360∘ )  12x, so that x  210∘ .
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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
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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∘



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, Section 1.1


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.




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So, the two angles have measures 30∘ and 150∘ .

17. Since the angles with measures 8x∘ and 4x∘ are assumed to be
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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∘ .
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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.
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So, the two angles have
measures 30∘and 60∘ .

19. Since       180∘, we know 20. Since       180∘, we know
that that
1 17∘ –33∘    180∘ and so,   30∘ . 1 10∘ –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∘ .


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