102 Higher Engineering Mathematics
(a) cot 17. 49 ◦=
1
tan17. 49 ◦
=3.1735
(b) cot 163◦ 52 ′=
1
tan163◦ 52 ′
=
1
tan163
52 ◦
60
=−3.4570
Problem 12. Evaluate, correct to 4 significant
figures:
(a) sin1.481 (b) cos( 3 π/ 5 ) (c) tan2. 93
(a) sin1.481 means the sine of 1.481radians. Hence
a calculator needs to be on the radian function.
Hence sin1. 481 =0.9960
(b) cos( 3 π/ 5 )=cos1. 884955 ···=−0.3090
(c) tan2. 93 =−0.2148
Problem 13. Evaluate, correct to 4 decimal
places:
(a) secant 5.37 (b) cosecantπ/ 4
(c) cotangentπ/ 24
(a) Again, with no degrees sign, it is assumed that
5.37 means 5.37radians.
Hence sec5. 37 =
1
cos 5. 37
=1.6361
(b) cosec(π/ 4 )=
1
sin(π/ 4 )
=
1
sin0. 785398 ...
=1.4142
(c) cot( 5 π/ 24 )=
1
tan( 5 π/ 24 )
=
1
tan0. 654498 ...
=1.3032
Problem 14. Find, in degrees, the acute angle
sin−^10 .4128 correct to 2 decimal places.
sin−^10 .4128 means ‘the angle whose
sine is 0.4128’
Using a calculator:
- Press shift 2. Press sin 3. Enter 0.4128
- Press ) 5. Press=The answer 24.380848......
is displayed
Hence, sin−^10. 4128 = 24. 38 ◦
Problem 15. Find the acute angle cos−^10 .2437 in
degrees and minutes
cos−^10 .2437 means ‘the angle whose
cosine is 0.2437’
Using a calculator:
- Press shift 2. Press cos 3. Enter 0.2437
- Press ) 5. Press=The answer 75.894979...
is displayed - Press◦”’ and 75◦ 53 ′ 41. 93 ′′is displayed
Hence, cos−^10. 2437 = 75. 89 ◦= 77 ◦ 54 ′
correct to the nearest minute.
Problem 16. Find the acute angle tan−^17 .4523 in
degrees and minutes
tan−^17 .4523 means ‘the angle whose
tangent is 7.4523’
Using a calculator:
- Press shift 2. Press tan 3. Enter 7.4523
- Press ) 5. Press =The answer 82.357318...
is displayed - Press◦”’ and 82◦ 21 ′ 26. 35 ′′is displayed
Hence, tan−^17. 4523 = 82. 36 ◦= 82 ◦ 21 ′
correct to the nearest minute.
Problem 17. Determine the acute angles:
(a) sec−^12 .3164 (b) cosec−^11. 1784
(c) cot−^12. 1273
(a) sec−^12. 3164 =cos−^1
(
1
2. 3164
)
=cos−^10. 4317 ...
=64.42◦or 64 ◦ 25 ′
or1.124radians
(b) cosec−^11. 1784 =sin−^1
(
1
1. 1784
)
=sin−^10. 8486 ...
=58.06◦or 58 ◦ 4 ′
or1.013radians