Answers and Hints for Selected Odd Numbered Problems

Exercises for Chapter I

1. acute; right; 90^o: obtuse; 156^o: The rest are not possible in a triangle.

3. (i) (a)      (b)      (c) 8      (d)

    (ii) (a) 4.24      (b) 9.53      (c) 8.00      (d) 5.74

5. x = 9/2 y = 6.

7. Yes

9. (a)

     (b) r = 2.823; u = 0.326; v = 0.138

13. Hint: Make repeated use of the theorem in Section 5.

15. Hint: Use Problem 14.

17. (a) 13      (b) 15      (c)      (d)

Exercises for Chapter II Sections 1 and 2

1. (a)      (b)            (d)

3. (a)

5. |G + H| = 5.

9 (a) The line OU.      (b) The line through O perpendicular to OU.

11.

15. (a)      (b)      (c)      (d)

17. (a) Yes;      (b) Yes;      (c) Yes.

19 (b)

Exercises for Chapter II Sections 3, 4, and 5

1. (a)      (c) -1 - i;

(d) -9i;      (e)

5. -7 - 8i.

7.

9.

11. (a) 56 + 33i;      (b) 16 + 63i.

13.

15.

19.

21.

23. (a) 12 + 5i;      (b) 33 + 56i;      (c) -12 - 5i;      (d) 7 + 24i;      (e) 63 + 16i.

25.

27. (c)

Exercises for Chapter II Sections 6 and 7

3.

9.

11. 10.55

13. (a) 53^o;      344^o;      200^o;      102^o.

     (b) 16.5 miles on a bearing of 44^o.

     (c) 31.5 miles on a bearing of 192^o.

Exercises for Chapter III Section 1

1. (a) a = -5; b = -3.

     (b)

3. a = -3; b = 2;

5.

7. (a)      (b) -12/13;      (c) -3/2;      (d) -15/17

11. HINT: Make use of Euler formula and its conjugate.

Exercises for Chapter III Section 2

3. for any integer n.

5.

Exercises for Chapter III Section 3

3.

Exercises for Chapter III Section 4

1. cos(38.4^o) = 0.7837;      sin(38.4^o) = 0.6211;      tan(38.4^o) = 0.7926;

sec(38.4^o) = 1.2760;      csc(38.4^o) = 1.6099;      cot(38.4^o) = 1.2617.

3. cos(-0.447) = 0.9017;      sin(-0.447) = -0.4323;      tan(-0.447) = -0.4794;

sec(-0.447) = 1.1090;      scs(-0.447) = -2.3134;      cot(-0.447) = -2.0861.

5. 1.150

13. Distance is 342.3 m and the angle is 27.5^o.