186 Basic Engineering Mathematics
and if
tan A = 3.5984 then A = tan
−1 3.5984 = 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, sin 43
◦ 39
sin 43
◦ 39
= sin 43
39
60
◦
= sin 43.65
◦
= 0.6903
This answer can be obtained using the calculator as
follows:
1. Press sin
2. Enter 43
3. Press ◦ ”’
4. Enter 39
5. Press ◦ ”’
6. Press )
7. Press =
Answer = 0.6902512...
Problem 9. Determine, correct to 3 decimal
places, 6 cos 62 ◦ 12
6 cos 62
◦ 12
= 6 cos 62
12
60
◦
= 6 cos62.20
◦
= 2.798
This answer can be obtained using the calculator as
follows:
1. Enter 6
2. Press cos
3. Enter 62
4. Press ◦ ”’
5. Enter 12
6. Press ◦ ”’
7. Press )
8. Press = Answer = 2.798319...
Problem 10. Evaluate sin 1.481, correct to 4
significant figures
sin 1.481 means the sine of 1.481 radians. (If there is no
degrees sign, i.e. ◦ , then radians are assumed). Therefore
a calculator needs to be on the radian function.
Hence, sin 1.481 = 0.9960
Problem 11. Evaluate cos(3π/5), correct to 4
significant figures
As in Problem 10, 3π/5 is in radians.
Hence, cos(3π/5) = cos 1.884955 ... = −0.3090
Since, from page 166, πradians = 180 ◦ ,
3π/5 rad =
3
5
× 180 ◦ = 108 ◦ .
i.e. 3π/5 rad = 108 ◦ . Check with your calculator that
cos 108 ◦ = −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, tan 2.93 = −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
−1 0.4128 in
degrees, correct to 2 decimal places
sin
−1 0.4128 means ‘the angle whose sine is 0.4128’.
Using a calculator,
1. Press shift
2. Press sin
3. Enter 0.4128
4. Press )
5. Press =
The answer 24.380848... is displayed.
Hence, sin
−1 0.4128 = 24.38 ◦ correct to 2 decimal
places.
Problem 14. Find the acute angle cos
−1 0.2437 in
degrees and minutes
cos −1 0.2437 means ‘the angle whose cosine is 0.2437’.
Using a calculator,
1. Press shift
2. Press cos
3. Enter 0.2437
4. Press )
5. Press =
The answer 75.894979... is displayed.
6. Press ◦ ”’ and 75 ◦ 53 41.93 is displayed.
Hence, cos −1 0.2437 = 75.89 ◦ = 77 ◦ 54 correct to the
nearest minute.
Problem 15. Find the acute angle tan −1 7.4523 in
degrees and minutes
tan −1 7.4523 means ‘the angle whose tangent is 7.4523’.
Using a calculator,
1. Press shift
2. Press tan
3. Enter 7.4523
4. Press )
5. Press =
The answer 82.357318... is displayed.
6. Press ◦ ”’ and 82 ◦ 21 26.35 is displayed.
Hence, tan −1 7.4523 = 82.36 ◦ = 82 ◦ 21 correct to the
nearest minute.
and if
tan A = 3.5984 then A = tan
−1 3.5984 = 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, sin 43
◦ 39
sin 43
◦ 39
= sin 43
39
60
◦
= sin 43.65
◦
= 0.6903
This answer can be obtained using the calculator as
follows:
1. Press sin
2. Enter 43
3. Press ◦ ”’
4. Enter 39
5. Press ◦ ”’
6. Press )
7. Press =
Answer = 0.6902512...
Problem 9. Determine, correct to 3 decimal
places, 6 cos 62 ◦ 12
6 cos 62
◦ 12
= 6 cos 62
12
60
◦
= 6 cos62.20
◦
= 2.798
This answer can be obtained using the calculator as
follows:
1. Enter 6
2. Press cos
3. Enter 62
4. Press ◦ ”’
5. Enter 12
6. Press ◦ ”’
7. Press )
8. Press = Answer = 2.798319...
Problem 10. Evaluate sin 1.481, correct to 4
significant figures
sin 1.481 means the sine of 1.481 radians. (If there is no
degrees sign, i.e. ◦ , then radians are assumed). Therefore
a calculator needs to be on the radian function.
Hence, sin 1.481 = 0.9960
Problem 11. Evaluate cos(3π/5), correct to 4
significant figures
As in Problem 10, 3π/5 is in radians.
Hence, cos(3π/5) = cos 1.884955 ... = −0.3090
Since, from page 166, πradians = 180 ◦ ,
3π/5 rad =
3
5
× 180 ◦ = 108 ◦ .
i.e. 3π/5 rad = 108 ◦ . Check with your calculator that
cos 108 ◦ = −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, tan 2.93 = −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
−1 0.4128 in
degrees, correct to 2 decimal places
sin
−1 0.4128 means ‘the angle whose sine is 0.4128’.
Using a calculator,
1. Press shift
2. Press sin
3. Enter 0.4128
4. Press )
5. Press =
The answer 24.380848... is displayed.
Hence, sin
−1 0.4128 = 24.38 ◦ correct to 2 decimal
places.
Problem 14. Find the acute angle cos
−1 0.2437 in
degrees and minutes
cos −1 0.2437 means ‘the angle whose cosine is 0.2437’.
Using a calculator,
1. Press shift
2. Press cos
3. Enter 0.2437
4. Press )
5. Press =
The answer 75.894979... is displayed.
6. Press ◦ ”’ and 75 ◦ 53 41.93 is displayed.
Hence, cos −1 0.2437 = 75.89 ◦ = 77 ◦ 54 correct to the
nearest minute.
Problem 15. Find the acute angle tan −1 7.4523 in
degrees and minutes
tan −1 7.4523 means ‘the angle whose tangent is 7.4523’.
Using a calculator,
1. Press shift
2. Press tan
3. Enter 7.4523
4. Press )
5. Press =
The answer 82.357318... is displayed.
6. Press ◦ ”’ and 82 ◦ 21 26.35 is displayed.
Hence, tan −1 7.4523 = 82.36 ◦ = 82 ◦ 21 correct to the
nearest minute.