104 Higher Engineering Mathematics
- (a) cosecant 213◦ (b) cosecant 15. 62 ◦
(c) cosecant 311[◦ 50 ′
(a)− 1. 8361 (b) 3. 7139
(c)− 1. 3421
]
- (a) cotangent71◦(b) cotangent151. 62 ◦
(c) cotangent321[◦ 23 ′
(a) 0. 3443 (b)− 1. 8510
(c)− 1. 2519
]
- (a) sine
2 π
3
(b) cos1.681 (c) tan3. 672
[
(a) 0. 8660 (b)− 0. 1010
(c) 0. 5865
]
- (a) sec
π
8
(b) cosec 2.961 (c) cot2. 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).
- sin−^10. 2341
[
13. 54 ◦, 13 ◦ 32 ′,
0 .236rad
]
- cos−^10. 8271
[
34. 20 ◦, 34 ◦ 12 ′,
0 .597rad
]
- tan−^10. 8106
[
39. 03 ◦, 39 ◦ 2 ′,
0 .681rad
]
- sec−^11. 6214
[
51. 92 ◦, 51 ◦ 55 ′,
0 .906rad
]
- cosec−^12. 4891
[
23. 69 ◦, 23 ◦ 41 ′,
0 .413rad
]
- cot−^11. 9614
[
27. 01 ◦, 27 ◦ 1 ′,
0 .471rad
]
- InthetriangleshowninFig.11.12,determine
angleθ, correct to 2 decimal places.
[29. 05 ◦]
9
5
Figure 11.12
- InthetriangleshowninFig.11.13,determine
angleθin degrees and minutes. [20◦ 21 ′]
23
8
Figure 11.13
In Problems 17 to 20, evaluate correct to 4 signifi-
cant figures.
- 4cos56◦ 19 ′−3sin21◦ 57 ′ [1.097]
18.
11 .5tan49◦ 11 ′−sin90◦
3cos45◦
[5.805]
19.
5sin86◦ 3 ′
3tan14◦ 29 ′−2cos31◦ 9 ′
[−5.325]
20.
6 .4cosec 29◦ 5 ′−sec81◦
2cot12◦
[0.7199]
- Determine the acute angle, in degrees and
minutes, correct to the nearest minute, given
by sin−^1
(
4 .32sin42◦ 16 ′
7. 86
)
[21◦ 42 ′]
- If tanx= 1 .5276, determine secx,cosecx,
and cotx. (Assumexis an acute angle)
[1.8258, 1.1952, 0.6546]
In Problems 23 to 25 evaluate correct to 4 signifi-
cant figures
23.
(sin 34◦ 27 ′)(cos 69◦ 2 ′)
(2tan53◦ 39 ′)
[0.07448]
- 3cot14◦ 15 ′sec23◦ 9 ′ [12.85]
25.
cosec27◦ 19 ′+sec45◦ 29 ′
1 −cosec27◦ 19 ′sec45◦ 29 ′
[−1.710]
- 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
]