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1. sin A = 1; cos A =

3. (i.)

ᎠᎪ . 4. (i.) ; (ii)

BA

(vi.)

2.

DB BA
CB' CA'

BD
BC

1. 179 ft.

2. 346 ft.

3. 86.6 ft.

4. 138.5 ft.

5. 7 ft.

6. 60°; 173 ft.

4.

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3. +

5.

1. 60°.

2. - 100°.

(x.)

6. Of the smaller angle, the sine = Of the larger angle, the sine

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7. Of the smaller angle, the sine =

(v.)

BA AC

EA EC'

DB BA AE (vii.) or

CD

CB CA

1

√3

3√41

25

(ii.)

-1.

- 1.

or

DC
BD'

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CD CB
CB' CA'

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AD AB
AB AC

=

1

√3

Of the larger angle, the sine = √3, cosine, tangent = √3. 9. BC= √3; sin A = {√3; cos A = }; tan A = √3. v 11. AC√2; sin B =√};

1

√3

sin A

3. 0°.

4. - 260°.

7.

8.

or

ᎠᏴ BC
(xi.) or
AB AC

V.

(iii.)

VII.

7. 63.17 yds.

8. 192.8 ft.

9. 34.15 ft.

10. 73.2 ft.

11. 86.6 ft.

12. 1524 yds.

XI.

9. +

+

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10. +

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1

√2

1

+ √3.

ᎠᏴ BA

CD' CB

DB BC

AD' AB

13,

13, cosine = 13, tangent=f1⁄2•
, tangent = 42.

cosine =

√3
, cosine = tangent =
"
2

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(iv) AB

AE

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2.

+1.

1

5. 115°.

6. 410°.

ᎠᎪ .

BD

(xii.)

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1

√5

15.

11.

;

12.

BE

AE

13. 173.2 yds.

14. 373 ft.

1

14.

2

√5

(iv.)

AD AB or ; (v.) AB AC'

BA AC (ix.) or EB EA'

; 2.

√3 a

3 b

30°.

16.

17. About 523.6 miles.

13. +

DB BC.

AB' AC'

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;+1. .

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1

15 -1; 1; +

2'

2

- 330°.

16. 36°; 150°; - 210°; 17. 45°; 135°; - 225°;

- 315°.

18. 60°; 120°; - 240°; - 300°. - 30°; — 150°; 210°; 330°.

19.

1.

2.

cot A = +

sin (90° + A)=

csc (90° + 4):

2. sin B

XV. (a).

sin A = √1 - cos2 A; tan A= ±

cos A
V1 - cos2 A

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cot A
√cot2 A +1

tan (90° + A) = - cot A; sec (90° + A) = −√cot A + 1;
/cot2 4+1

cot A

; cos A =

3

Va2 9. sin 0 =

a

3. sin (180°- A) = ±

/sec2 A sec A tan (180° - A) = ± √sec A 1, etc. Vesc2 A-1 CSC A sin A; cos A±√1 - sin2 A; tan A= ±

4. sin A=

1 csc A

5. sin A =

=

6. See answers to Example 1.

(b) 1. tan A+ ; cosec A = }.

=

=2d2;

; cos 0 =

; sin e=3.

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12. cos 0; tan e

=

cot B =

; sec A =

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cot @=

7.

-

1

2√2

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20. 20°; 160°; 380°; 520°.
15π.

21.

;

; 13 π;

4

22.

;

; 22 π ; 27 π.

25. The tangent..

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1 cos A

b

; cos (90° + A) — ·

V1 - cos2 A
cos A

;

1. 45°; 135°. 2. 30°; 150°; 210°; 330°.

3. 45°; 135°; 225°; 315°.

4. 60°; 120°; 240°; 300°.

5. 30°; 150°; 210°; 330°. 6. 30°; 150°; 210°; 330°. 7. 30°; 150°.

;

c2b2

; csc A= ±

cos (180° - A) =

XVI.

tan A =

1

V1 - cos2 A

1

;

√cot2 A +1

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cot @=

8.

1 sec A

1
Vesc2 A-1
sin A
√1 - sin2 A

3. sin A; sec A = §.

4.

; sin 0 =

26. No.

1

√15

a

+ Va2 + 1

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8. 45°; 315°; 0°; 180°.

9. 90°; 270°; 60°; 120°. 10. 60°; 120°; 240°; 300°. 11. 45°; 225°.

12. 90°; 70°; 45°; 315°.

18. 0°; 180°; 45°; 135°.

etc.

etc.

√15

1

Va2 + 1

14. 45°; 135°; 225°; 315°. 15. 45°; 135°. 16. 30°; 330°. 17. 30°; 150°. 18. 60°; ± 120°; ± 240°; ± 300°. 19. 0°; 180°; 180°; - 360°.

21. nw ; 2 nx +¦; (2n + 1)π − ☎ ·

π

20. 2n; (n any integer).

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1. 3.7040.

1. 7.669.

2. 3.809.

3. 47.32.

076

; }; - 1;

2.

1. cos A = ; cos } A = √3. 2. 45°; 60°; 75°.

3. 135°; 30°; 15°. 4. 3. 6. 1+ √3. 7. 120°. 8. 9. 120°. 10. 90°; 36° 52'. 11. 130° 27'.

12. 125° 6'.

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6. cos + cos 2 0.

12.

5. 3. -3; 6, 2. 4.

2. 45740.2.

4. 55460.

5. 12.03.

6. .04023.

XXI.

22. nπ +

1. 60°. 2. 120°. 3. 30°; 150°. 4. 135°.

3. sin (2a + 3 B) + sin (2 a − 3 ß).

4. cos 2a + cos 2 B.

XXV.

5. 14. 120°.

XXVI.

3.

13. 4 cos2 sin 20.

XXVIII.

XXIX.

2; 4;

3;

π

2

XXX.

7.

cos 40 sin 2 0.

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18. 60°; 75°; 6 yds.
21. 15:8√3:4√5 +6.

XXXI.

3. 2492830.

(cos 30 - cos 50).

13. 120°.

14. a = 1.

15. C 30°; a = √3 + 1 ; b = 2.
16. A = 75°; a = b = √3 + 1.
17. C 60° or 120°.

XXXII.

7. 8287.

8. 1165.

9. .3107.

1; -3; - 4.

-1; 5; 2; 3; -3.

1. 3.55169; .87251; 3.63548.

2. 4.93662; 1.98320; 3.54654. 4. 6.83181; 7.51129.

5. 45°; 135°.

13. 1.

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3. 2.65920; 2.54926; 3.85941.

6. 120°.

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