Page 92 - WCS - Electrical

Exercise 1.6.25
Workshop Calculation & Science - Electronics Mechanic
Trigonometry - Measurement of angles
Introduction:
Trigonometry is the branch of mathematics which deals
Radius of the circle makes an angle (r) = 1 Radian
with the study of measurement and relationship of the
o
360
C
three sides and three angles of a triangle.
=
ie :
1Radian
r
Units:
Measurement of Angles
o
360
r
2π
=
There are three systems of measuring the angle:
1Radian
r
(i) Sexagesimal System
o
360
This is called British System. In this system, one right
2π =
1Radian
angle is divided into 90 equal parts which are called
degrees.Each part is divided into 60 parts which are called
2π Radian = 360°
minutes.Each minute is divided into 60 parts which are
π Radian = 180°
called seconds.The parts so divided respectively are called:
o
One degree (1°), one minute (1') and one second (1")
180
1 Radian =
= 90° (90 degrees)
It means 1 right angle
π
π
1 degree (1°) = 60' (60 minutes)
o Radian
1° =
1 minute (1') = 60" (60 seconds)
180
Examples
In Trigonometry, mostly this system is used.
1 Convert 45°36’20” into degree and decimal of degree.
(ii) Centesimal System
60 second = 1 minute
This is called French System. In this system, the right
angle is divided into 100 equal parts which are called
20
= 0.333’
20 second =
grades. Each grade is divided into 100 minutes and each
60
minute is divided into 100 seconds.
60 minute = 1 degree
Parts so divided are respectively called:
36.333
One grade (1 g), one minute (1' ), one second (1").
= 0.606°
36.333 minute =
60
It means 1 right angle = 100 grades (100g)
45 36’20” = 45.606°
0
1 grade (1 g) = 100 minutes (100’)
2 Convert 24.59° into degree, minute and second
1 minute (1') = 100 seconds (100")
90° = 100g (because each is a right
1 degree = 60 minute
angle)
0.59 degree = 0.59 x 60 = 35.4’
This system is easier than Sexagesimal System. But to
1 minute = 60 second
use this system many other systems will have to be devised
that is why this system is not used.
0.4 minute = 60 sec x 0.4
(iii) Circular System
= 24”
In this system, the unit of measuring angles is radian. It
Therefore 24.59° = 24 35’24”
0
is that angle which is formed at the centre and is formed
of an arc of length equal to radius in a circle. Circumference makes an angle (2πr) = 360°
3 Change 50 37’30” into degrees
0
There is one constant ratio between the circumference By changing angle degrees into decimals
and dia of a circle. This is represented by π . 30
nce
Circumfere 30” = 60 = 0.50’ WORKSHOP CALCULATION & SCIENCE - CITS
Diameter = constant point = π 37’30” = 37.5’
Circumference = π x dia
= 2πr (where r is radius of the circle) 37.5’ 37.5’ = = 37.5 = 0.625°
= 0.625
0
22 60
π = 50°37’30” 0 = 50.625° 0
7 50 37’30” = 50.625
4 Convert 23° 25’ 32” into radians 59 4 180 4
4 Convert 23 25’ 32” into radians
0
4 Convert 23 25’ 32” into radians
0
4 Convert 23
0 25’ 32” into radians
4
0
0 25’ 32” into radians
0
4 Convert 23
π
0 25’ 32” into radians
180 x
180 4π
4 Convert 23 25’ 32” into radians 4 4 π 4 radian = 180 180 πx 180 4 degree
4 radian =
4 degree
We know 1 = 60’ = 3600”
We know 1° = 60’ = 3600”
4 Convert 23 25’ 32” into radians
0
4 Convert 23 0
4 Convert 23 25’ 32” into radians
7
π
We know 1 = 60’ = 3600”
180x
7
4π degree
0
4π radian = x
0 = 60’ = 3600”
π radian =
7
We know 1
4 4 π radian = 7π
180 x π degree
0
4 4 π degree
We know 1 = 60’ = 3600”
0 = 60’ = 3600”
0
We know 1
x π degree
π radian
π degree
π radian = π 7π
0 = 60’ = 3600”
Therefore 23 25’32”
We know 1 = 60’ = 3600”
0
We know 1 0
7
Therefore 23°25’32” 7 7 7 7 7 π radian = = π π π x x 7 7 7 7 π degree
π
7
We know 1 = 60’ = 3600”
= 102.9 degree
Therefore 23 25’32”
0
0 0 25’32”
Therefore 23
0
= 102.9 degree
Therefore 23 25’32” 0 25’32” 4 = 102.9 degree 4
Therefore 23
0
025’32”
Therefore 23 0 25’ 32” into radians
4 Convert 23
= 102.9 degree
= 102.9 degree
Therefore 23 25’32”
Therefore 23 25’32”
180
= 102.9 degree
= 102 0.9 x 60’
= 102.9 degree
0
25
= 102 0.9 x 60’
= 102.9 degree
0
⎛
32 ⎞
x
π degree
= 102
⎛
25
0
=
0 0.9 x 60’
= 102
⎛
23
degrees
+
+
0
0 0.9 x 60’
⎟
= 102
⎜
We know 1 = 60’ = 3600” 25 32 ⎞ 32 ⎞ egrees 7 π radian = 0 0 0.9 x 60’
⎛23
= 102 0 7π
⎛ 25 +
=

+
⎜
0 0.9 x 60’
25 32 ⎞ d ⎟
= 102 54’
= 102 0.9 x 60’

=
32 ⎞ egrees
= 102 54’
= 102 0.9 x 60’
+
⎜ 60
0
⎛ 23 + 3600 ⎠ d
32
⎝23
25 25
⎜
0 =
32 ⎞ ⎞d ⎟ egrees

⎛ ⎛ + + 360060
= 102
egrees
0 54’
⎜ ⎝
25 + ⎟ ⎠
0

23
= 102 54’
60
=
Therefore 23 25’32” = + 23 + + 60 3600 ⎠ 32 ⎞ d ⎟ ⎟ ⎟ degrees 8 Convert 0.8357 radian into degrees
= 102
0 54’
0
⎜ 23
⎟ degrees
23 +
+ +
+3600 ⎠
⎜ = ⎝
=⎜60
degrees
= 102.9 degree
⎝
0 54’ 54’
3600 ⎠
⎝
= 102
= 102 0
= 102 54’
60 60 32
1500+
82800+
60 3600
⎝
3600 ⎠
3600 ⎠ ⎠
8 Convert 0.8357 radian into degrees
1500+
82800+
8 Convert 0.8357 radian into degrees
= 102 0.9 x 60’
= = 82800 ⎝ ⎝ 1500++ 1500+ 32 32 8 Convert 0.8357 radian into degrees
32
0
82800+
8 Convert 0.8357 radian into degrees
32
1500+
82800+
82800+ 25
1500+32
82800
8 Convert 0.8357 radian into degrees
3600
8 Convert 0.8357 radian into degrees
82800+1500++
180
= = = = = ⎜ ⎛ 3600 1500+ 32 32 ⎞ ⎟ degrees 8 Convert 0.8357 radian into degrees
32
23
180
==
+
+
3600
180
degree
1 radian =
3600
= 102 54’
3600
0
84332
180
⎝
3600
1 radian = π
3600
180 degree
180
1 radian = π
84332
1 radian = degree
180 degree
= = 84332 3600360060 ⎠ 1 radian = 180 degree
π
84332
degree
84332
1 radian = =
3600
=
1 radian π
degree
84332
degree
1 radian = π
84332 1500++
84332
= 3600 82800 32 8 Convert 0.8357 radian into degrees
π
=
π π
=
= = =3600
180
3600
180
3600
3600
180
3600
3600 3600
= π radians
180
180
0
0.8357 radian = π x 0.8357 degree
180
0 = π radians
But 180
But 180° = radians 0.8357 radian = π x 0.8357 degree
But 180 0
180
180
0 = π radians
But 180
1 radian =
180 degree
0.8357 radian = π x 0.8357 degree
But 180
But 180 = π radians
0
84332
But 180 0 = π radians
πx 0.8357 degree
Therefore 23.4255 degrees
0.8357 radian = π
0.8357 radian = π x 0.8357 degree
But 180 = π radians
But 180
= π radians
=
0.8357 radian = π x 0.8357 degree
Therefore 23.4255 degrees 0 0 = π radians 0.8357 radian = π x 0.8357 degree
0.8357 radian = π x 0.8357 degree
Therefore 23.4255 degrees
0
Therefore 23.4255 degrees
= 47.88 0
Therefore 23.4255 degrees 23.4255 = 47.88 0 180 0 0 0
3600
Therefore 23.4255 degrees
= 47.88
= 47.88
Therefore 23.4255 degrees
Therefore 23.4255 degrees
= 47.88
Therefore 23.4255 degrees
= 47.88
= 47 0.88 x 60’
0
23.4255
= 47.88
0 0
= 47 0.88 x 60’
= 47.88
0
23.4255 radians π
=
0 0.88 x 60’
= 47
0
=
But 180 23.4255 π π radians 0.8357 radian = 0.88 x 60’
= π radians
0
= 47
23.4255
= 47 0 π x 0.8357 degree
0
0 0.88 x 60’
= 47
= 180
23.4255 radians π
= 47 52.80’
0 0.88 x 60’
radians
23.4255
= 180
=
= 47 0.88 x 60’
0
23.4255 radians π
= 47 0.88 x 60’
0
= = 180
=
π radians
0 52.80’
= 47
0
180
radians
Therefore 23.4255 degrees 180 π π radians = 47 52.80’ 0
0 52.80’
= 47
0 52.80’
= 47
0
180 22
23.4255
= 47.88
180 22
23.4255
0 52.80’
= 47 52’0.8 x 60”
= 47 52.80’
= 47 52.80’
= 47 0
23.4255
0
23.4255 22radians x
= = 23.4255 180 radians x 22 = 47 52’0.8 x 60”
22
0 52’0.8 x 60”
= 47
0
= 47
7
22radians
23.4255 x
0 52’0.8 x 60”
0 0 52’0.8 x 60”
0
= 47
= 180
= 47
= = 180 23.4255radians x radians π 7 22 radians radians = 47 52’48” 0 52’0.8 x 60”
23. x 7
= 47 0 0.88 x 60’
23.4255 224255 x
= 47 52’48”
= 47 52’0.8 x 60”
=
= = = 180
= 47 52’0.8 x 60”
0
radians
x x
180 7
180
radians
= 47
0 52’48”
0
7
180
= 0.4089 radians
= 47 52’48”
180
180
= 47
0
0 0 52’48”
= 0.4089 radians 7 7 7 9 Convert 2.752 radian into degrees
180
= 47
= 47 0 52.80’
0 52’48”
= 47 52’48”
= 0.4089 radians
= 47 52’48”
= 0.4089 radians
= 0.4089 radians
= 0.4089 radians
23.4255
22
9 Convert 2.752 radian into degrees
= 0.4089 radians
= 0.4089 radiansdians 9 Convert 2.752 radian into degrees
5 Convert 87 19’ 57” into Radian.
= 0.4089 ra
9 Convert 2.752 radian into degrees
0
= 47 52’0.8 x 60”
9 Convert 2.752 radian into degrees
0
5 Convert 87 19’ 57” into Radian.
x

radians
=
0
9 Convert 2.752 radian into degrees
4 Convert 23 25’ 32” into radians
180
0
0 19’ 57” into Radian.
9 Convert 2.752 radian into degrees
5 Convert 87
9 Convert 2.752 radian into degrees
0
5 Convert 87 19’ 57” into Radian.
180
180
4
4
0
5 Convert 87
019’ 57” into Radian.
180
1 Radian =
degree
0 19’ 57” into Radian.
5 Convert 87 19’ 57” into Radian.
7′
5
0
5 Convert 87 0
x
180 degree
5 Convert 87 19’ 57” into Radian.
π radian =
180
5 Convert 87°19’ 57” into Radian. 75 ′ 7 1 Radian = 180 = 47 52’48” π degree
180degree
π
1 Radian =
We know 1 = 60’ = 3600” 75 ′
0
180
1 Radian = π
1 Radian = degree
180 π degree
= 0.4089 radians
19’57” = 19’ + 75 ′
7
7
19’57”
degree
π
7′
degree
1 Radian = =
19’57” = 19’ +
5 7′
1 Radianπ
1 Radian = π
degree
5 5
4 Convert 23 0 = 19’ + 60 5 7′ 7′ 9 Convert 2.752 radian into degrees
0 25’ 32” into radians
19’57” = 19’ + 60
π
19’57” = 19’ +
19’57” = 19’ + 60
Therefore 23 25’32”
4
4
180
= 102.9 degree
19’57” = 19’ +
60
19’57”
= 19’ + 60
19’57” = 19’ +
5 Convert 87 19’ 57” into Radian. 2.7520 radian = 180 180 π π 180 0 7 π degree
0
x
π radian =
x 2.752 degree
2.7520 radian =
0 = 19’ + 0.95’
60 60
60
We know 1 = 60’ = 3600”
= 19’ + 0.95’
180 x 2.752 degree
180
180 π
7
2.7520 radian = π
= 19’ + 0.95’
180
= 102 0.9 x 60’
180degree
1 Radian = x 2.752 degree
= 19’ + 0.95’
2.7520 radian =
7′
= 19’ + 0.95’
x 2.752 degree
25
5
⎛
= 19’ + 0.95’
x 2.752 degree
π
= 19.95’
2.7520 radianπ
= 19’ + 0.95’
Therefore 23 25’32” = 19’ + 0.95’ 32 ⎞ ⎟ degrees 2.7520 radian = π 180 x 2.752 degree
x 2.752 degree
2.7520 radian = π
x 2.752 degree
2.7520 radian = = π
= 19’ + 0.95’++=
23
0

⎜
= 19.95’
19’57” = 19’ +
π = 102.9 degree
π π
= 19.95’
= 102 54’
0
0
= 157.7
60
= 157.7 0
= 19.95’
= 157.7
0
= 19.95’
= 157.7
= 19.95’
= 157.7
0
0
= 19.95’ o
= 19.95’ ⎝ ⎛ 19.95 60 3600 ⎠ = 157.7 x 60’ 0 0 0.9 x 60’
= 102
180
0 0
= 157.7 x 60’
= 157.7
19.95
= 19.95’ o
= 157.7
0
32 ⎞
= 157.7
0
1500+
= 19’ + 0.95’
x 2.752 degree
87°19.95’ = 87° +
= 157.7
19.95
0 x 60’
=
0
23
+
87°19.95’ = 87° + 82800+ o 25 o o + o o o 32 ⎟ degrees 8 Convert 0.8357 radian into degrees
= 157.7
= ⎜ 19.95
0 x 60’
= 157.7
2.7520 radian = 0
19.95
0 0 x 60’
π
= 157.7 054’
= 102
87°19.95’ = 87° + 60
0 x 60’
= 157 42’
19.95
= 157.7 x 60’
60
19.95
= 157.7 x 60’
⎝ 60
87°19.95’ = 87° +
87°19.95’ = 87° +
19.95 3600 ⎠
3600
0
= 87° +
180
87°19.95’ 87°19.95’ = 87° + 60 = 157 42’ 0 0 42’ 0
= 157
87°19.95’ = 87° +
= 19.95’ 60
= 157 42’
87°19.95’ = 87° + 60
0 42’
0
= 157
= 157.7
1 radian =
degree
= 87° + 0.332° = 87.33°
84332+
0 42’ 42’
= 157
60 60 1500+
60
82800
3
= 157 42’
= 157 0
= 87° + 0.332° = 87.33° 32 8 Convert 0.8357 radian into degrees
π
3
= 87° + 0.332° = 87.33°
= =
π
o
10 Convent π
= 87° + 0.332° = 87.33°
= 87° + 0.332° = 87.33°
3 radian into degrees
= 157.7 x 60’
= 87° + 0.332° = 87.33°
0
87°19.95’ = 87° + 19.95 10 Convent 3 3 radian into degrees
3600 3600
= 87° + 0.332° = 87.33°
5
π
3π radian into degrees
= 87° + 0.332° = 87.33°
180
= 87° + 0.332° = 87.33°
10 Convent π
10 Convent 5
π
10 Convent radian into degrees
3 3 π radian into degrees
π
radian
10 Convent 1 radian =
180 degree
π radian into degrees
5
1° = π
π radian into degrees
1° = 0 radian 60 10 Convent 5 5 5 5 π radian into degrees
84332
10 Convent 5
π
= 157 42’
0
1° 180
π
π
But 180 =
= π radians
π π radian
180
= radian
0.8357 radian = π x 0.8357 degree
radian
1° = 180
radian
radian
1° 1° = 180 = 87° + 0.332° = 87.33° 1 Radian = 180 180
1° 180
=
1° = 3600
degree
radian
radian
1° = = 180
3
180
1 Radian =
180 degree
180
180
π
π
Therefore 23.4255 degrees 10 Convent 1 Radian = degree 0
180
180 degree
180 180
1 Radian =
π
π radian into degrees
1 Radian = π
= 47.88
180 degree
π
degree
0 x 87.33 radian
87.33° =
5
degree
1 Radian = =
degree
1 Radianπ
87.33° = 180 = π radians 3 0.8357 radian π π π π x 0.8357 degree
π π
1 Radian = π
But 180π x 87.33 radian
π =
π x 87.33 radian
87.33° =
87.33° = 180
π π 23.4255
180
= 47 0.88 x 60’
1° = x 87.33 radian
3
0
radian
3
87.33° = 180
x 87.33 radian
π
radians
x 87.33 radian
π
87.33° =
180
87.33° = 180 x 87.33 radian
x 87.33 radian
87.33°
=
87.33° = = 180
Therefore 23.4255 degrees x 87.33 radian 3 3 π 3 radian = 180 180 π 0 3 degree
x
180 3 π
180
3 radian =
180 x
0 3 degree
= 47.88
= 1.524 radian
180
180
180 180
3π
= 47 5
3π radian = π
= 1.524 radian 5 5 π radian = π 180 52.80’ degree
3 3 1 Radian = x 5
180 x π degree
3 3 π
π radian =
180degree degree
= 1.524 radian
x 5
5
π
π degree
= 1.524 radian
π degree
x x
= 1.524 radian
π radian = π 5
π degree
= 1.524 radian
x 5
π radianπ

= 1.524 radian 22
π 23.4255
π radian = = π
5
0
5
= 1.524 radian
π
= 1.524 radian
5 5
π π 52’0.8 x 60”
6 Convert 67°11’43” into Radian
= 47
x 87.33 radian
6 Convert 67°11’43” into Radian = = 23.4255 x radians π radians 5 5 5 5 = 108 0 = 47 0 0.88 x 60’
87.33° =
= 108 0
6 Convert 67°11’43” into Radian
= 108
0
7
180
6 Convert 67°11’43” into Radian
= 108
6 Convert 67°11’43” into Radian
0 0 52.80’
6 Convert 67°11’43” into Radian 180 180 22 3 π radian = = 47 0 0 52’48”
= 108
0
0
3
0
180
6 Convert 67°11’43” into Radian
= 108
= 47
4
6 Convert 67°11’43” into Radian
3′
= 108
6 Convert 67°11’43” into Radian
= 108
4
3′
π degree
x
23.4255
3′
= 0.4089 radians
4
11’43” = 11’ + 34 ′
= 1.524 radian
π 52’0.8 x 60”
Assignment
4
11’43” = 11’ +
3′ x
= 60
4 3′
11’43” = 11’ +
9 Convert 2.752 radian into degrees
4 4
11’43” 11’43” = 11’ + 60 180 3′ 3′ 7 radians Assignment 5 = 47 0 5
Assignment
= 11’ +
11’43” = 11’ +
Assignment
11’43” = 11’ + 60
Assignment
Assignment
60
11’43” = 11’ +
11’43” = 11’ + 60
= 47
5 Convert 87 19’ 57” into Radian.
0
Assignment
6 Convert 67°11’43” into Radian 60 60 Convert into Degree = 108 0 52’48”
0
Assignment
Convert into Degree
60
180
= 11’ + 0.716’
= 0.4089 radians
Convert into Degree
= 11’ + 0.716’
1 Radian =
7′
= 11’ + 0.716’ 4 5 3′ Convert into Degree degree
= 11’ + 0.716’
9 Convert 2.752 radian into degrees
Convert into Degree
= 11’ + 0.716’
= 11’ + 0.716’
Convert into Degree
= 11’ + 0.716’
Convert into Degree
Convert into Degree
0 = 11.72’
1 12 Radian
= 11’ + 0.716’
19’57” = 19’ +
11’43” = 11’ +
= 11’ + 0.716’
= 11.72’
5 Convert 87 19’ 57” into Radian. 1 12 Radian π
Assignment
= 11.72’
1 12 Radian
60
60
1 12 Radian
= 11.72’
= 11.72’ 11.72 5 o 7′ Convert into Radians 180
= 11.72’
1 12 Radian
= 11.72’
1 12 Radian
= 11.72’
1 12 Radian
Convert into Radians
1 12 Radian 1 Radian =
180 degree
11.72
= 11.72’ o
Convert into Radians
= 19’ + 0.95’o
2.7520 radian = π
19’57” = 19’ + 11.72
Convert into Radians
67°11.72’ = 67° +
Convert into Radians
o
= 11’ + 0.716’ o
π
67°11.72’ = 67° +
11.72
Convert into Radians
60
Convert into Radians
11.72
Convert into Radians
= 67° +
67°11.72’ 67°11.72’ = 67° + 60 11.72 o o o 2 78 Convert into Degree = 157.7 x 2.752 degree
11.72
67°11.72’ = 67° + 60
67°11.72’ = 67° +
11.72
o
= 19.95’
67°11.72’ = 67° + 60
2 78 o
1 12 Radian
67°11.72’ = 67° +
180
= 11.72’ 60
2 78
67°11.72’ = 67° + 60
o
0
2 78
= 67° + 0.195°
o
2 78
60 60
o
= 19’ + 0.95’
60
220'
0
2 78 78
2 78
o o
= 67° + 0.195°
3 47 0
= 67° + 0.195°
= 67° + 0.195°
19.95
= 67° + 0.195° 11.72 o o 3 47 20' 0 o 0 20' 2.7520 radian = π x 2.752 degree
Convert into Radians
= 67° + 0.195°
3 47
= 157.7 x 60’
0
= 67.2°
= 67° + 0.195°
= 67° + 0.195°
3 47 20'
0 0 20'
0
3 47
= 67.2°
= 67° + 0.195°
= 19.95’
87°19.95’ = 87° +
= 67.2°
336' 45"
3 47 47
67°11.72’ = 67° + 4 52 36' 45" = 157.7 0
0 20' 20'
3 47 20'
0
4 52 0
60
= 67.2°
0
4 52
= 67.2°
o 36' 45"
= 67.2° 60 o 4 52 36' 45" = 157 42’
0
= 67.2°
= 67.2°
π
= 67.2°
4 52
0
2 7836' 45"
π
0
0 36' 45"
4 52 52 36' 45"
438"
π
0
0 0
19.95
radian
4 52 36' 45"
= 157.7 x 60’
0
5 25 0
= 67° + 0.195°
1° = π radian
π
1° = 180 = 87° + 0.332° = 87.33° 5 25 38" 0 0 0 0 Convent 3 π radian into degrees
5 25
π
0 38"
87°19.95’ = 87° +
π π radian
1° =
1° = 180
5 25 38"
3 47 20'
0
1° = radian
5 25 38"
radian
radian60
0 38"
1° = 180
5 10
5 25 25 38"
= 157 42’
Convert into degree, minute and seconds
0
1° =
5 25 38"
1° = 180
radian
= 67.2°
5
180
180
π
Convert into degree, minute and seconds
4 52 36' 45"
Convert into degree, minute and seconds
π 180 180 π radian Convert into degree, minute and seconds
0
Convert into degree, minute and seconds
radian
1° =
Convert into degree, minute and seconds
π
= 87° + 0.332° = 87.33°
Convert into degree, minute and seconds
Convert into degree, minute and seconds
π
180
π
67.2° = 180 x 67.2 radian 6 46.723 o 3
67.2° = π x 67.2 radian
6 46.723 o
180
π
π π x 67.2 radian
67.2° =
6 46.723
67.2° = 180 x 67.2 radian 79 7 68.625 o 0 Convent 5 π radian into degrees
o
1° = x 67.2 radian
radian
6 46.723
10 o
6 46.723
67.2° = 180
1 Radian =
degree
x 67.2 radian
5 25 38" o
67.2° = 180 π
67.2° 180
x 67.2 radian
6 46.723
67.2° = = 180
o
x 67.2 radian
6 46.723
6 46.723
o o
π
180 π
= 1.173 radian
180
= 1.173 radian
1° =
7 68.625 o
180 radian
7 68.625
= 1.173 radian
o
Convert into degree, minute and seconds
87.33° = 180
7 68.625
o
= 1.173 radian
= 1.173 radian
7 68.625
o
4
7 68.625
π CITS : WCS - Electrical - Exercise 7
= 1.173 radian
o
7 68.625
180
8 0.1269 Radians
= 1.173 radian
o o
7 68.625
= 1.173 radian
7 Convert π
into degrees
180 degree
x 67.2 radian
4 π
67.2° =
7 Convert 4 4 radian 4 radian into degrees x 87.33 radian 8 0.1269 Radians 3 1 Radian = 180 x 3 π degree
8 0.1269 Radians
6 46.723
o
8 0.1269 Radians
180 π
π radian = π
7 Convert
8 0.1269 Radians
into degrees
4
7
into degrees
= 1.524 radian
7 Convert π radian π
8 0.1269 Radians
7 Convert 7 4 4 radian π radian into degrees 9 2.625 Radians 5 π 5
8 0.1269 Radians
9 2.625 Radians
8 0.1269 Radians
7 Convert π
radian into degrees
x 87.33 radian
87.33° =
into degrees
7 Convert π radian π
7 Convert 7
radian into degrees
7
7
180
9 2.625 Radians
7 68.625
180
= 1.173 radian
7
9 2.625 Radians
180
9 2.625 Radians
7 7
180
6 Convert 67°11’43” into Radian 10 3/5 Radians o 3 π = 108 0 x 3 π degree
9 2.625 Radians
180
9 2.625 Radians
10 3/5 Radians
degree
1 radian =
9 2.625 Radians radian =
180 deg
180ree
1 radian =
4
π
180
= 1.524 radian
180
1 radian =
180 degree
10 3/5 Radians
= π
8 0.1269 Radians
degree
1 radian
10 3/5 Radians
radian into degrees
7 Convert π 1 radian = π degree 10 3/5 Radians 5 π 5
degree 34 ′
10 3/5 Radians
1 radianπ
10 3/5 Radians
degree
1 radian = = π
degree
1 radian =
10 3/5 Radians
60
7
π π1’ +
11’43”
π = 1
WCS - Electronics Mechanic : (NSQF - Revised Syllabus 2022) - 1 Year : Exercise 1.6.25
st
60 6 Convert 67°11’43” into Radian 60 9 2.625 Radians = 108 0
WCS - Electronics Mechanic : (NSQF - Revised Syllabus 2022) - 1 Year : Exercise 1.6.25
st
WCS - Electronics Mechanic : (NSQF - Revised Syllabus 2022) - 1
st Year : Exercise 1.6.25
Assignmentst
60 60 60 WCS - Electronics Mechanic : (NSQF - Revised Syllabus 2022) - 1 Year : Exercise 1.6.25
60
180
WCS - Electronics Mechanic : (NSQF - Revised Syllabus 2022) - 1
st
st Year : Exercise 1.6.25
st Year : Exercise 1.6.25
60 60
WCS - Electronics Mechanic : (NSQF - Revised Syllabus 2022) - 1 Year : Exercise 1.6.25
3′
4
WCS - Electronics Mechanic : (NSQF - Revised Syllabus 2022) - 1 st
WCS - Electronics Mechanic : (NSQF - Revised Syllabus 2022) - 1 Year : Exercise 1.6.25
degree
1 radian =
10 3/5 Radians
Convert into Degree
= 11’ + 0.716’
11’43” = 1
π1’ +
Assignment
60
1 12 Radian
= 11.72’
60 WCS - Electronics Mechanic : (NSQF - Revised Syllabus 2022) - 1 Year : Exercise 1.6.25
st
= 11’ + 0.716’ o Convert into Degree
Convert into Radians
= 11.72’
67°11.72’ = 67° + 11.72 1 12 Radian
60 2 78 o
11.72
= 67° + 0.195° o Convert into Radians
67°11.72’ = 67° + 3 47 20'
0
= 67.2° 60 2 78 o 0
= 67° + 0.195° 4 52 36' 45"
π
3 47 20'
0
0
1° = 180 radian 5 25 38"
= 67.2°
4 52 36' 45"
0
5 25 38"
0
1° = π π radian Convert into degree, minute and seconds
67.2° = 180 6 46.723 o
x 67.2 radian
180 Convert into degree, minute and seconds
π
= 1.173 radian 7 68.625 o
67.2° = x 67.2 radian 6 46.723 o
4 180
7 Convert π radian into degrees 8 0.1269 Radians
o
7 = 1.173 radian 7 68.625
4 9 2.625 Radians
7 Convert π 1 radian = 180 degree 8 0.1269 Radians

radian into degrees
10 3/5 Radians
7 π 9 2.625 Radians
180
60 WCS - Electronics Mechanic : (NSQF - Revised Syllabus 2022) - 1 Year : Exercise 1.6.25
st
10 3/5 Radians
degree
1 radian =
π
60 WCS - Electronics Mechanic : (NSQF - Revised Syllabus 2022) - 1 Year : Exercise 1.6.25
st