Understanding Engineering Mathematics

6.3.2 Definitions of the trig ratios

A.

θ 0 π/2 π/3 π/4 π/6

sinθ 01

√

3

2

1

√

2

1

2

tanθ 0nd

√

31

1

√

3

secθ 1nd2

√

2

2

√

3

cosθ 10

1

2

1

√

2

√

3

2

cotθ nd 0

1

√

3

1

√

3

cosecθ nd 1

2

√

3

√

22

(nd = not defined)

B.cos and sec are even; sin, cosec, tan, cot all odd.

C. (i) (− 1 )nsinx (ii) (− 1 )ncosx (iii) tanx

(iv) (− 1 )(n−^1 )/^2 cosxifnodd,(− 1 )n/^2 sinxifneven

(v) (− 1 )n/^2 cosxifneven,(− 1 )

n+ 1

(^2) sinxifnodd
(vi) tanxifneven, – cotxifnodd.
6.3.3 Sine and cosine rules and the solution of triangles
(i)B= 50 ° a= 7 .36, c= 6. 78
(all answers to 2 decimal places)
(ii) Two solutions:
C= 53. 46 A= 86. 54 °, a= 12. 42
C= 126. 54 °, A= 13. 36 °, a= 2. 9
(iii)C= 14. 9 °, B= 125. 1 °, b= 6. 36
(the obtuse solution forCis inadmissible in this case)
(iv)A= 44. 42 °, B= 57. 11 °, C= 78. 47 °
(v)a= 3 .88, B= 55. 98 °, C= 84. 02 °
(vi)a=7, B= 21. 77 °, C= 38. 21 °