104 Higher Engineering Mathematics
5. (a) cosecant 213 ◦ (b) cosecant 15.62 ◦
(c) cosecant 311 ◦ 50
(a) −1.8361 (b) 3.7139
(c) −1.3421
6. (a) cotangent 71 ◦ (b) cotangent 151.62 ◦
(c) cotangent 321 ◦ 23
(a) 0.3443 (b) −1.8510
(c) −1.2519
7. (a) sine
2π
3
(b) cos 1.681 (c) tan 3.672
(a) 0.8660 (b) −0.1010
(c) 0.5865
8. (a) sec
π
8
(b) cosec 2.961 (c) cot 2.612
(a) 1.0824 (b) 5.5675
(c) −1.7083
In Problems 9 to 14, determine the acute angle
in degrees (correct to 2 decimal places), degrees
and minutes, and in radians (correct to 3 decimal
places).
9. sin −1 0.2341
13.54 ◦ , 13 ◦ 32 ,
0.236 rad
10. cos −1 0.8271
34.20 ◦ , 34 ◦ 12 ,
0.597 rad
11. tan −1 0.8106
39.03 ◦ , 39 ◦ 2 ,
0.681 rad
12. sec −1 1.6214
51.92
◦
, 51
◦ 55
,
0.906 rad
13. cosec −1 2.4891
23.69 ◦ , 23 ◦ 41 ,
0.413 rad
14. cot −1 1.9614
27.01 ◦ , 27 ◦ 1 ,
0.471 rad
15. In the triangle shown in Fig. 11.12, determine
angle θ, correct to 2 decimal places.
[29.05 ◦ ]
9
5
Figure 11.12
16. In the triangle shown in Fig. 11.13, determine
angle θ in degrees and minutes.
[20
◦ 21
]
23
8
Figure 11.13
In Problems 17 to 20, evaluate correct to 4 significant figures.
17. 4 cos 56 ◦ 19 − 3 sin21 ◦ 57
[1.097]
18.
11.5 tan49 ◦ 11 − sin 90 ◦
3 cos 45 ◦
[5.805]
19.
5 sin86 ◦ 3
3 tan14 ◦ 29 − 2 cos31 ◦ 9
[−5.325]
20.
6.4 cosec 29 ◦ 5 − sec 81 ◦
2 cot 12 ◦
[0.7199]
21. Determine the acute angle, in degrees and
minutes, correct to the nearest minute, given
by sin −1
4.32 sin 42 ◦ 16
7.86
[21 ◦ 42 ]
22. If tan x = 1.5276, determine sec x, cosec x,
and cot x. (Assume x is an acute angle)
[1.8258, 1.1952, 0.6546]
In Problems 23 to 25 evaluate correct to 4 significant figures
23.
(sin 34
◦ 27
)(cos 69
◦ 2
)
(2 tan 53 ◦ 39 )
[0.07448]
24. 3 cot 14 ◦ 15 sec 23 ◦ 9
[12.85]
25.
cosec 27 ◦ 19 + sec 45 ◦ 29
1 − cosec 27 ◦ 19 sec 45 ◦ 29
[−1.710]
26. Evaluate correct to 4 decimal places:
(a) sine (−125 ◦ ) (b) tan(−241 ◦ )
(c) cos(−49 ◦ 15 )
(a) −0.8192 (b) −1.8040
(c) 0.6528
5. (a) cosecant 213 ◦ (b) cosecant 15.62 ◦
(c) cosecant 311 ◦ 50
(a) −1.8361 (b) 3.7139
(c) −1.3421
6. (a) cotangent 71 ◦ (b) cotangent 151.62 ◦
(c) cotangent 321 ◦ 23
(a) 0.3443 (b) −1.8510
(c) −1.2519
7. (a) sine
2π
3
(b) cos 1.681 (c) tan 3.672
(a) 0.8660 (b) −0.1010
(c) 0.5865
8. (a) sec
π
8
(b) cosec 2.961 (c) cot 2.612
(a) 1.0824 (b) 5.5675
(c) −1.7083
In Problems 9 to 14, determine the acute angle
in degrees (correct to 2 decimal places), degrees
and minutes, and in radians (correct to 3 decimal
places).
9. sin −1 0.2341
13.54 ◦ , 13 ◦ 32 ,
0.236 rad
10. cos −1 0.8271
34.20 ◦ , 34 ◦ 12 ,
0.597 rad
11. tan −1 0.8106
39.03 ◦ , 39 ◦ 2 ,
0.681 rad
12. sec −1 1.6214
51.92
◦
, 51
◦ 55
,
0.906 rad
13. cosec −1 2.4891
23.69 ◦ , 23 ◦ 41 ,
0.413 rad
14. cot −1 1.9614
27.01 ◦ , 27 ◦ 1 ,
0.471 rad
15. In the triangle shown in Fig. 11.12, determine
angle θ, correct to 2 decimal places.
[29.05 ◦ ]
9
5
Figure 11.12
16. In the triangle shown in Fig. 11.13, determine
angle θ in degrees and minutes.
[20
◦ 21
]
23
8
Figure 11.13
In Problems 17 to 20, evaluate correct to 4 significant figures.
17. 4 cos 56 ◦ 19 − 3 sin21 ◦ 57
[1.097]
18.
11.5 tan49 ◦ 11 − sin 90 ◦
3 cos 45 ◦
[5.805]
19.
5 sin86 ◦ 3
3 tan14 ◦ 29 − 2 cos31 ◦ 9
[−5.325]
20.
6.4 cosec 29 ◦ 5 − sec 81 ◦
2 cot 12 ◦
[0.7199]
21. Determine the acute angle, in degrees and
minutes, correct to the nearest minute, given
by sin −1
4.32 sin 42 ◦ 16
7.86
[21 ◦ 42 ]
22. If tan x = 1.5276, determine sec x, cosec x,
and cot x. (Assume x is an acute angle)
[1.8258, 1.1952, 0.6546]
In Problems 23 to 25 evaluate correct to 4 significant figures
23.
(sin 34
◦ 27
)(cos 69
◦ 2
)
(2 tan 53 ◦ 39 )
[0.07448]
24. 3 cot 14 ◦ 15 sec 23 ◦ 9
[12.85]
25.
cosec 27 ◦ 19 + sec 45 ◦ 29
1 − cosec 27 ◦ 19 sec 45 ◦ 29
[−1.710]
26. Evaluate correct to 4 decimal places:
(a) sine (−125 ◦ ) (b) tan(−241 ◦ )
(c) cos(−49 ◦ 15 )
(a) −0.8192 (b) −1.8040
(c) 0.6528