Higher Engineering Mathematics, Sixth Edition

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:

1. Press shift 2. Press sin 3. Enter 0.4128


2. 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:

1. Press shift 2. Press cos 3. Enter 0.2437


2. Press ) 5. Press=The answer 75.894979...
   is displayed


3. 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:

1. Press shift 2. Press tan 3. Enter 7.4523


2. Press ) 5. Press =The answer 82.357318...
   is displayed


3. 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