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ANSWERS

ANSWERS

PLANE TRIGONOMETRY

a

a

с

; sec B

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с

a

=

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8

1 7 8

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ra; cot A 15; cot A 40; cot A 8ő ; cot A

39

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8.9 39

CSC A

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Exercise 1. Page 5

b 1. cos B = - ; tan B =-; cot B =

a

b 3. tan A. 4. cot A. 5. sec A.

6. CSC A. 7. sin A = }; cos A = $; tan A = \ ; cot A = t; sec A = ; csc A = 5 8. sin A = 13; cos A } } ; tan A

2; sec A { }; csc A = 12 9. sin A

i
17; tan A

15 ; sec A 1}; csc A = 1 10. sin A 4 1 ; tan A

42; sec A = 47: CSC A=41. 11. sin A 89; tan A

$$ ; sec A = 88; csc A 12, sin A

18%; tan A = { 1%; cot A = {f}; sec A = { }; tis. 13. a2 + 52

n2 1

2n

ma 1 14. sin A ==

; tan A =
; cot A =

;
na + 1
n2 +1

n? 1
na + 1

n2 + 1 sec A na - 1

2 n n2 - 1

n3 - 1 15. sin A = ; cos A =

tan A =

; cot A =
na +1
722 -1

2n
na + 1

na + 1
n2 -1

2n
m2 n2

m2 – 18 16. sin A

cos A =

tan A = ma + na

m2 + na
m2 + n2

m2 + n2
; CSC A =
m2
m2

m2 - na 17. sin A=

; cos A =
; tan A =

cotA=
m2 + na
ma + na

m2
m2 + na

ma + na sec A

m2 – m2 19. sin A } V2 = cos A ; tan 4 =1= cot A; sec A =v

=V2 = 20. sin A = { V5; cos A = { V5; tan A = 2; cot A = }; sec A=V5;

csc A = { V5. 21. sin A = }; cos A = }V5; tan A = V5; cot A = } V5; sec A = f V5;

CSC A = . 22. sin B = 14}; cos B = 145; tan B= cot B= ; sec B = o ;

csc B = 145 23. sin B = Pos; cos B= 15%; tan B= 1'os; cot B= 1099; sec B = 1%%;

OSC B 24. sin B

os; cos B = 6*; tan B= d'e; cot B=24; sec B = csc B

1

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P-9,

; cos B =

ز

2 P9

p+p4

; csc B=

2 pq

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COS A

sin B;

2 pa

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2 Vp

2 Vp

P-9 25. sin B =

cot B=

tan B =
P +9
P +9

P-9
pta
sec B =

P 9

Vp2 + 92
26. sin A =
= cos B; cot A =

= tanB;
p+q

Vp + 92

pta sec A=

= csc B; P +9

2 p
Vp + q?

pta
tan A=
= cot B; Csc A =

= sec B.

vp2 + 2
V p2 + P
27. sin A = <= cos B; cotA= tan B;

P
1

sec A = Vp +1 = csc B;
Vp +1

pa + P
tan A Vp=c
= cot B; CSC A =

= sec B.

P 28. 12.3. 37. 2.5; 1.5.

47. a =

4.501 ; b = 5.362. 29. 1.54. 38. 1.5 mi. ; 2 mi.

48. a=

6.8801 ; b = 8.1962. 30. 9.

40. a = 0.342 ; b = 0.94. 49. a = 160.75; b= 191.5. 31. 6800.

41. a = 1.368; h = 3.76. 50. a = 1.88; b = 0.684. 32. 4000.

42. a = 1.197; b = 3.29. 51. C = 2.128 ; b = 0.728. 33. 227.84.

43. a = 1.6416 ; b = 4.512. 52. C = 5.848; a = 5.494. 34. 3 V13; 9. 44. a = 2.565; b = 7.05.

53. C =

26.6; b= 9.1. 35. ?V3; 273. 45. a = 0.643; b= 0.766. 54. a = 412.05; c= 438.6. 36. 5; 3. 46. a = 1.929; b= 2.298. 55. 142.926 yd.

56. 1}; 24 ft.

COS A

sin B ;

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Exercise 2. Page 7 1. cos 60°. 5. cos 40°. 9. cos 30o. 13, cos 14° 30'. 17. cos 25o. 21. tan 29o. 2. sin 70°. 6. cot 30°. 10. sin 30°. 14. cot 7° 15'. 18. cot 10°. 22. sec 12o. 3. cot 50°. 7. csc 150. 11. cot 45°. 15. csc 21°45'. 19. csc 13°. 23. cos 1o. 4. Csc 65o. 8. sec 5o. 12. csc 45°. 16. sin 1° 50'. 20. sin 38°. 24. sin 4°. 25. csc 2°. 27. sin 71

29. 45°.

31. 30°.
26. cos 1210
28. cot 1.4°.

30. 45°.

32. 30°.

21. 1.

Exercise 3. Page 9 1. 0.5. 5. 1.1547. 9. 1.7320.

13. V2.

17. ? Vo. 2. 0.8660. 6. 2. 10. 0.5773. 14. } V6. 18. ] V2.

22. 3. 3. 0.5773. 7. 0.8660.

11. 2.

15. 73.

19. 13. 23. 13. 4. 1.7320. 8. 0.5. 12. 1.1547. 16. 3.

20. 13.

24. V3. 25. cos 27° 42' 20". 27. CSC 2° 27' g". 29. cos 14.2°. 31. cot 21.189. 26. cot 14° 31' 25". 28. sin 1° 59 33". 30. sin 7.25o. 32. csc 4.050. 33. 90°. 90° 40. 22° 30'.

43. V6. 47. 2 V3. 51. 1. 34. 60°. n+1 41. 18o.

44. V2.

48. 2. :52. V3. 35. 22° 30'. 38. 90°.

90° 42.

45. Vē.

-49. V3. 36. 18o. 39. 60°.

n+1 46. 3. 50. 1V3.

37.

Exercise 4.

Page 10 1. 0.0872. 7. 0.3584. 13. 0.9135. 19. 5.1446. 25. 1.0000. 31. 1.4396. 2. 0.2419, 8. 0.5000. 14. 0.9135. 20. 5.1446. 26. 1.0000. 32. 1.4396. 3. 0.3584. 9. 0.9945. 15. 0.8192. 21. 0.3839. 27. 1.0353. 33. 0.0038. 4. 0.5000. 10. 0.9945. 16. 0.8192. 22. 0.3839. 28. 1.0353. 34. 0.0054, 5. 0.0872. 11. 0.9703. 17. 11.4301. 23. 1.0000. 29. 4.8097. 35. 2 sec 10°. 6. 0.2419. 12. 0.9703. 18. 11.4301. 24. 1.0000. 30. 4.8097. 36. 2 csc 10°.

37. 2 cos 15°.
38. 3 sin 20° > sin (3 x 20°) and > sin (2 x 20°).
39. 3 tan 10° <tan (3 109) and > tan (2 x 10°).

um.
40. 3 cos 10° > cos (3 x 10°) and > cos (2 x,109).
41. No.
42. The sin, tan, sec increase and the cos, cot, csc decrease.

[blocks in formation]
[blocks in formation]

Exercise 7. Page 16
15. 63o. 22. 411.4 ft. 29. 6 in.
16. 70°. 23. 383 ft.

30. 28.19 ft.; 21.21 ft.; 17. 54°. 24. 43o.

12.68 ft.; 30 ft.; 0 ft 18. 60°. 25. 7.794 in. 31. 60°; 0°. 19. 70°. 26. 166.272 sq.in. 32. 25°; 65o. 20. 84o. 27. 5.657.

33. 30° and 60° ; 21. 60°. 28. 27.71 ft.

31° and 59o.

34. 749.9 ft.
Exercise 8. Page 19
11. 45o. 16. 64o.

20. 159.7 ft.
12. 8o. 17. 148 ft. 8 in. 21. 45° ; 90°; 45°
13. 9o. 18. 29o.

22. 15.76 ft. 14. 19o. 19. 2.517 mi; 23. 6.14 ft. 15. 22o.

3.916 mi. 24. 1.03 in.

[blocks in formation]

Exercise 9. Page 20

1. 26.11.
2. 12.35.
3. 162.6.

4. 85.81.
5. 544.0.
6. 26.84.

7. 26.60. 10. 25°.
8. 68.80. 11. 28.87 ft.
9. 45°.

12. 428.4 ft.

13. 113 ft. 14. 123.6 ft.

1. 40.40. 2. 61.77. 3. 101.2.

13. 26.11 ft.

Exercise 10. Page 21
7. 41°,

10. 57.74 ft.
8. 60°.

11. 1369 ft.
9. 22.65 ft. 12. 91.64 ft.

4. 33.63.
5. 55.50.
6. 339.4.

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