Basic Engineering Mathematics, Fifth Edition

186 Basic Engineering Mathematics

and if

tanA= 3 .5984 thenA=tan−^13. 5984 =74.47◦

each correct to 2 decimal places.

Use your calculator to check the following worked

problems.

Problem 8. Determine, correct to 4 decimal

places, sin43◦ 39 ′

sin43◦ 39 ′=sin43

39

60

◦

=sin43. 65 ◦=0.6903

This answer can be obtained using thecalculatoras

follows:

1. Press sin 2. Enter 43 3. Press◦”’


2. Enter 39 5. Press◦”’ 6. Press )


3. Press= Answer=0.6902512...

Problem 9. Determine, correct to 3 decimal

places, 6 cos62◦ 12 ′

6 cos 62◦ 12 ′=6 cos 62

12

60

◦

=6cos62. 20 ◦=2.798

This answer can be obtained using thecalculatoras

follows:

1. Enter 6 2. Press cos 3. Enter 62


2. Press◦”’ 5. Enter 12 6. Press◦”’


3. Press ) 8. Press= Answer=2.798319...

Problem 10. Evaluate sin 1.481, correct to 4

significant figures

sin 1.481 means the sine of 1.481radians. (If there is no

degreessign,i.e.◦,thenradiansareassumed).Therefore

a calculator needs to be on the radian function.

Hence, sin1. 481 =0.9960

Problem 11. Evaluate cos( 3 π/ 5 ), correct to 4

significant figures

As in Problem 10, 3π/5isinradians.

Hence,cos( 3 π/ 5 )=cos1. 884955 ...=−0.3090

Since, from page 166,πradians= 180 ◦,

3 π/5rad=

3

5

× 180 ◦= 108 ◦.

i.e. 3π/5rad= 108 ◦. Check with your calculator that

cos108◦=− 0. 3090

Problem 12. Evaluate tan 2.93, correct to 4

significant figures

Again, since there is no degrees sign, 2.93 means 2.93

radians.

Hence,tan2. 93 =− 0. 2148

It is important to know when to have your calculator on

either degrees mode or radian mode. A lot of mistakes

can arise from this if we are not careful.

Problem 13. Find the acute angle sin−^10 .4128 in

degrees, 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 ◦correct to 2 decimal
   places.

Problem 14. 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.

6. Press◦”’ and 75◦ 53 ′41.93′′is displayed.
   Hence,cos−^10. 2437 = 75. 89 ◦= 77 ◦ 54 ′correct to the
   nearest minute.

Problem 15. Find the acute angle tan−^17 .4523 in

degrees and minutes

tan−^17 .4523means‘theanglewhosetangentis7.4523’.

Using a calculator,

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


2. Press ) 5. Press =

The answer 82.357318...is displayed.

6. Press◦”’ and 82◦ 21 ′26.35′′is displayed.
   Hence,tan−^17. 4523 = 82. 36 ◦= 82 ◦ 21 ′correct to the
   nearest minute.