Page 90 - WCS - Electrical

Workshop Calculation & Science - Electronics Mechanic
Exercise 1.6.25
Workshop Calculation & Science - Electronics Mechanic
Workshop Calculation & Science - Electronics Mechanic Exercise 1.6.25 Exercise 1.6.25
Trigonometry - Measurement of angles
Trigonometry - Measurement of angles
Trigonometry - Measurement of angles
WORKSHOP CALCULATION & SCIENCE - CITS
Introduction:
Introduction:
Workshop Calculation & Science - Electronics Mechanic Exercise 1.6.25 Circumference makes an angle (2πr) = 360°
Circumference makes an angle (2πr) = 360°
Introduction:
Circumference makes an angle (2πr) = 360°
Trigonometry is the branch of mathematics which deals
Radius of the circle makes an angle (r) = 1 Radian
Trigonometry is the branch of mathematics which deals
Exercise 1.6.25
Workshop Calculation & Science - Electronics Mechanic
Radius of the circle makes an angle (r) = 1 Radian
EXERCISE 7: Trigonometrydeals
Trigonometry - Measurement of angles with the study of measurement and relationship of the C 360 o
Trigonometry is the branch of mathematics which
Radius of the circle makes an angle (r) = 1 Radian
with the study of measurement and relationship of the
with the study of measurement and relationship of the
three sides and three angles of a triangle. o
C
Trigonometry - Measurement of angles
three sides and three angles of a triangle.
360 o
Workshop Calculation & Science - Electronics Mechanic Exercise 1.6.25 ie : r = 1Radian
360
C
three sides and three angles of a triangle.
=
Units: ie :
Introduction:
Circumference makes an angle (2πr) = 360°
1Radian
=
ie :
r
Units:
Trigonometry - Measurement of angles
1Radian
r
Units:
Trigonometry - Measurement of angles Radius of the circle makes an angle (r) = 1 Radian 2π r 360 o
Trigonometry is the branch of mathematics which deals
Introduction:
Measurement of Angles
Circumference makes an angle (2πr) = 360°

Measurement of Angles
with the study of measurement and relationship of the o 2π r r 360 o =
2π
Measurement of Angles
360 o
Trigonometry is the branch of mathematics which deals
There are three systems of measuring the angle:
Radius of the circle makes an angle (r) = 1 Radian
=
three sides and three angles of a triangle.
There are three systems of measuring the angle:
Introduction: Introduction: ie : C = 360 r = 1Radian r 1Radian
with the study of measurement and relationship of the Circumference makes an angle (2πr) = 360°
There are three systems of measuring the angle:
(i) Sexagesimal System r
o
1Radian
360
three sides and three angles of a triangle.
rC
Units:
Trigonometry is the branch of mathematics which deals with the study of measurement and relationship of the
(i) Sexagesimal System
Trigonometry is the branch of mathematics which deals Radius of the circle makes an angle (r) = 1 Radian 1Radian 360 o
(i) Sexagesimal System
o
three sides and three angles of a triangle.
This is called British System. In this system, one right
with the study of measurement and relationship of the ie : r = 1Radian 360 2π =
360 o
Measurement of Angles
Units:
o
This is called British System. In this system, one right
360
o
2π
r
2π =
360
This is called British System. In this system, one right
C
three sides and three angles of a triangle. angle is divided into 90 equal parts which are called 1Radian
1Radian
2π =
Units:
angle is divided into 90 equal parts which are called
=
1Radian
There are three systems of measuring the angle: ie : degrees.Each part is divided into 60 parts which are called
=
Measurement of Angles
o
angle is divided into 90 equal parts which are called
1Radian
r r 1Radian
degrees.Each part is divided into 60 parts which are called r
Units: Measurement of Angles 2π 360 2π Radian = 360°
2π Radian = 360°
degrees.Each part is divided into 60 parts which are called
=
2π Radian = 360°
There are three systems
(i) Sexagesimal Systemof measuring the angle: minutes.Each minute is divided into 60 parts which are
minutes.Each minute is divided into 60 parts which are
called seconds.The parts so divided respectively are called:
Measurement of Angles minutes.Each minute is divided into 60 parts which are r 360 o 1Radi oan π Radian = 180°
360
There are three systems of measuring the angle:
called seconds.The parts so divided respectively are called: r 2π
π Radian = 180°
(i) Sexagesimal System
This is called British System. In this system, one right 2π = π Radian = 180°
called seconds.The parts so divided respectively are called:
=
o
There are three systems of measuring the angle: One degree (1°), one minute (1') and one second (1") 1 Radian = 180 o
1Radian
360
i Sexagesimal System
r
1Radian
o
angle is divided into 90 equal parts which are called
One degree (1°), one minute (1') and one second (1")
This is called British System. In this system, one right
180 o
2π =
It means 1 right angle 1 Radian = 180
degrees.Each part is divided into 60 parts which are called
(i) Sexagesimal System One degree (1°), one minute (1') and one second (1") 2π Radian = 360°adian = 90° (90 degrees) π
1R
1 Radian =
angle is divided into 90 equal parts which are called
This is called British System. In this system, one right angle is divided into 90 equal parts which are called
= 90° (90 degrees)
It means 1 right angle
o
minutes.Each minute is divided into 60 parts which are 360 π π
It means 1 right angle
= 90° (90 degrees)
1 degree (1°) = 60' (60 minutes)
degrees.Each part is divided into 60 parts which are called
degrees.Each part is divided into 60 parts which are called minutes.Each minute is divided into 60 parts which
This is called British System. In this system, one right 2π Radian = 360° π π
1 degree (1°) = 60' (60 minutes)
π Radian = 180°
2π =
called seconds.The parts so divided respectively are called:
are called seconds.The parts so divided respectively are called: 1Radian
π
minutes.Each minute is divided into 60 parts which are
1 degree (1°) = 60' (60 minutes)
angle is divided into 90 equal parts which are called 1 minute (1') = 60" (60 seconds) 1° = 180 o Radian
1° =
o Radian
180 o Radian
1 minute (1') = 60" (60 seconds)
π Radian = 180°
One degree (1°), one minute (1') and one second (1")
called seconds.The parts so divided respectively are called:
degrees.Each part is divided into 60 parts which are called 2π Radian = 360° 180 o 1° = 180 Examples
1 minute (1') = 60" (60 seconds)
One degree (1°), one minute (1’) and one second (1”)
1 Radian =
Examples
minutes.Each minute is divided into 60 parts which are In Trigonometry, mostly this system is used.
In Trigonometry, mostly this system is used.
Examples
o
= 90° (90 degrees)
It means 1 right angle
One degree (1°), one minute (1') and one second (1")
π 180
In Trigonometry, mostly this system is used.
It means 1 right angle
(ii) Centesimal System
called seconds.The parts so divided respectively are called: = 90° (90 degrees) π Radian = 180° 1 Convert 45°36’20” into degree and decimal of degree.
1 Radian =
1 Convert 45°36’20” into degree and decimal of degree.
π
(ii) Centesimal System
1 degree (1°) = 60' (60 minutes) 1 Convert 45°36’20” into degree and decimal of degree.
= 90° (90 degrees)
It means 1 right angle
π
(ii) Centesimal System
1 degree (1°)
o
o Radian
1° =
One degree (1°), one minute (1') and one second (1") = 60’ (60 minutes) This is called French System. In this system, the right 60 second = 1 minute
180
60 second = 1 minute
1 minute (1') = 60" (60 seconds)
1 degree (1°) = 60' (60 minutes)
This is called French System. In this system, the right
180 π 60 second = 1 minute
angle is divided into 100 equal parts which are called
This is called French System. In this system, the right
= 90° (90 degrees)
It means 1 right angle 1 minute (1’) = 60” (60 seconds) 1 Radian = 1° = 180 o Radian 20 20 second = 20 = 0.333’
Examples
π
angle is divided into 100 equal parts which are called
In Trigonometry, mostly this system is used.
1 minute (1') = 60" (60 seconds)
grades. Each grade is divided into 100 minutes and each
angle is divided into 100 equal parts which are called
20 second = 20
= 0.333’
grades. Each grade is divided into 100 minutes and each
1 degree (1°) = 60' (60 minutes) 1 Convert 45°36’20” into degree and decimal of degree. 60
π
In Trigonometry, mostly this system is used.
20 second =
= 0.333’
Examples
grades. Each grade is divided into 100 minutes and each
minute is divided into 100 seconds. 60
(ii) Centesimal System
In Trigonometry, mostly this system is used.
o Radian
1° =
minute is divided into 100 seconds.
60
1 minute (1') = 60" (60 seconds) 1 Convert 45°36’20” into degree and decimal of degree. 60 minute = 1 degree
180
minute is divided into 100 seconds.
ii Centesimal System
60 minute = 1 degree
60 second = 1 minute
60 minute = 1 degree
This is called French System. In this system, the right Examples Parts so divided are respectively called:
(ii) Centesimal System
Parts so divided are respectively called:
In Trigonometry, mostly this system is used. 60 second = 1 minute 36.333 36.333 minute = 36.333 = 0.606°
Parts so divided are respectively called:
This is called French System. In this system, the right angle is divided into 100 equal parts which are called
angle is divided into 100 equal parts which are called
One grade (1 g), one minute (1' ), one second (1").
20
36.333
This is called French System. In this system, the right
One grade (1 g), one minute (1' ), one second (1"). 20 second =
= 0.333’
1 Convert 45°36’20” into degree and decimal of degree.
36.333 minute =
grades. Each grade is divided into 100 minutes and each minute is divided into 100 seconds.
= 0.606°
grades. Each grade is divided into 100 minutes and each
(ii) Centesimal System One grade (1 g), one minute (1' ), one second (1"). It means 1 right angle = 100 grades (100g) 60
36.333 minute =
60 = 0.606°
angle is divided into 100 equal parts which are called
60 20
It means 1 right angle = 100 grades (100g)
minute is divided into 100 seconds. 60 second = 1 minute = 0.333’ 60
20 second =
Parts so divided are respectively called:
It means 1 right angle = 100 grades (100g)
grades. Each grade is divided into 100 minutes and each
0
This is called French System. In this system, the right 60 minute = 1 degree 45 36’20” = 45.606° 45 36’20” = 45.606°
1 grade (1 g) = 100 minutes (100’)
60
0
1 grade (1 g) = 100 minutes (100’)
minute is divided into 100 seconds.
Parts so divided are respectively called:
45 36’20” = 45.606°
angle is divided into 100 equal parts which are called 1 minute (1') = 100 seconds (100")
20
0
One grade (1 g), one minute (1’ ), one second (1”).
1 grade (1 g) = 100 minutes (100’)
60 minute = 1 degree
36.333
grades. Each grade is divided into 100 minutes and each 20 second = 60 = 0.333’ = 0.606° 2 Convert 24.59° into degree, minute and second
2 Convert 24.59° into degree, minute and second
1 minute (1') = 100 seconds (100")
Parts so divided are respectively called:
One grade (1 g), one minute (1' ), one second (1").
1 minute (1') = 100 seconds (100")
2
It means 1 right angle
90° = 100g (because each is a right
minute is divided into 100 seconds. = 100 grades (100g) 36.333 minute = Convert 24.59° into degree, minute and second 1 degree = 60 minute
60
36.333
90° = 100g (because each is a right
60 minute = 1 degree
It means 1 right angle = 100 grades (100g) = 100 minutes (100’) 36.333 minute = 1 degree = 60 minute
One grade (1 g), one minute (1' ), one second (1").
angle)
90° = 100g (because each is a right
= 0.606° = 60 minute
1 grade (1 g)
Parts so divided are respectively called: angle) 45 36’20” = 45.606° 1 degree 0.59 degree = 0.59 x 60 = 35.4’
60
0
1 grade (1 g) = 100 minutes (100’) angle) This system is easier than Sexagesimal System. But to
0.59 degree = 0.59 x 60 = 35.4’
It means 1 right angle = 100 grades (100g)
36.333
0.59 degree = 0.59 x 60 = 35.4’
1 minute (1’)
One grade (1 g), one minute (1' ), one second (1"). = 100 seconds (100”) use this system many other systems will have to be devised 1 minute = 60 second
36.333 minute =
45 36’20” = 45.606°
= 0.606°
This system is easier than Sexagesimal System. But to 0
2 Convert 24.59° into degree, minute and second
1 minute (1') = 100 seconds (100")
This system is easier than Sexagesimal System. But to
1 grade (1 g) = 100 minutes (100’)
1 minute = 60 second
60
use this system many other systems will have to be devised
90°
It means 1 right angle = 100 grades (100g) = 100g (because each is a right angle) 1 minute = 60 second 0.4 minute = 60 sec x 0.4
that is why this system is not used.
use this system many other systems will have to be devised
90° = 100g (because each is a right
2 Convert 24.59° into degree, minute and second
1 degree = 60 minute
1 minute (1') = 100 seconds (100")
that is why this system is not used.
0.4 minute = 60 sec x 0.4
0
that is why this system is not used.
This system is easier than Sexagesimal System. But to use this system many other systems will have to be
1 grade (1 g) = 100 minutes (100’) angle) 45 36’20” = 45.606° 0.4 minute = 60 sec x 0.4 = 24”
(iii) Circular System
90° = 100g (because each is a right
0.59 degree = 0.59 x 60 = 35.4’
(iii) Circular System
1 degree = 60 minute
= 24”
devised that is why this system is not used.
(iii) Circular System
1 minute (1') = 100 seconds (100") angle) 2 Convert 24.59° into degree, minute and second= 24” Therefore 24.59° = 24 35’24”
This system is easier than Sexagesimal System. But to
In this system, the unit of measuring angles is radian. It
0
1 minute = 60 second
0.59 degree = 0.59 x 60 = 35.4’
In this system, the unit of measuring angles is radian. It
Therefore 24.59° = 24 35’24”
iii Circular System
use this system many other systems will have to be devised
is that angle which is formed at the centre and is formed
90° = 100g (because each is a right 1 degree = 60 minute 0 0
In this system, the unit of measuring angles is radian. It
Therefore 24.59° = 24 35’24”
This system is easier than Sexagesimal System. But to
is that angle which is formed at the centre and is formed
of an arc of length equal to radius in a circle.
0.4 minute = 60 sec x 0.4
that is why this system is not used. angle)formed at the centre and is formed 1 minute = 60 second 3 Change 50 37’30” into degrees
is that angle which is
In this system, the unit of measuring angles is radian. It is that angle which is formed at the centre and is formed
0
use this system many other systems will have to be devised 3 Change 50 37’30” into degrees
0
of an arc of length equal to radius in a circle. 0.59 degree = 0.59 x 60 = 35.4’
of an arc of length equal to radius in a circle.
3 Change 50 37’30” into degrees
0
of an arc of length equal to radius in a circle.
(iii) Circular System
that is why this system is not used.
This system is easier than Sexagesimal System. But to 0.4 minute = 60 sec x 0.4 By changing angle degrees into decimals
There is one constant ratio between the circumference
= 24”
By changing angle degrees into decimals
1 minute
There is one constant ratio between the circumference = 60 second
use this system many other systems will have to be devised Therefore 24.59° = 24 35’24” 30
By changing angle degrees into decimals
There is one constant ratio between the circumference
and dia of a circle. This is represented by
There is one constant ratio between the circumference and dia of a circle. This is represented by π . .
(iii) Circular System
In this system, the unit of measuring angles is radian. It
= 24”
0
and dia of a circle. This is represented by π .
30
that is why this system is not used. 0.4 minute = 60 sec x 0.4 30” = 30 = 0.50’ 30” = 60 = 0.50’
and dia of a circle. This is represented by π .
is that angle which is formed at the centre and is formed
nce
In this system, the unit of measuring angles is radian. It
Therefore 24.59° = 24 35’24”
Circumfere 0
Circumfere
nce
60 = 0.50’
30” =
of an arc of length equal to radius in a circle.
(iii) Circular System Circumfere = constant point = π 3 Change 50 37’30” into degrees = constant point = π 37’30” = 37.5’
0
= 24”
nce
60
Diameter
= constant point = π
is that angle which is formed at the centre and is formed
Diameter
37’30” = 37.5’
Diameter
3 Change 50 37’30” into degrees
By changing angle degrees into decimals
of an arc of length equal to radius in a circle.
There is one constant ratio between the circumference
0
In this system, the unit of measuring angles is radian. It Therefore 24.59° = 24 35’24” = π x dia = 37.5’
Circumference
0
37’30”
= π x dia
Circumference
and dia of a circle. This is represented by
Circumference = π . x dia
is that angle which is formed at the centre and is formed By changing angle degrees into decimals 37.5
30
= π x dia
Circumference
= 2πr (where r is radius of the circle)
There is one constant ratio between the circumference
37.5
= 2πr (where r is radius of the circle) 30” =
of an arc of length equal to radius in a circle. = 2πr (where r is radius of the circle) 60 = 0.50’ 37.5’ = 37.5 = 0.625 0 0 37.5’ = 60 = 0.625 0
3 Change 50 37’30” into degrees
0
Circumfere
and dia of a circle. This is represented by
= 2π . r (where r is radius of the circle)
nce
30
60 = 0.625
22 37.5’ =
= constant point = π
22
π = 0.50’
There is one constant ratio between the circumference By changing angle degrees into decimals 60 50 37’30” = 50.625 0
30” =
=
Diameter
Circumfere
60
22
nce
0
7
50 37’30” = 50.625
0
and dia of a circle. This is represented by π π = 7 37’30” = 37.5’ 50 37’30” = 50.625 0 0
= constant point = π =
π . =
30
0
Diameter
Circumference
= π x dia
7
37’30” = 37.5’
37.5
Circumfere = 2πr (where r is radius of the circle) 30” = 60 = 0.50’ = 0.625 0 59 59
59
nce
= π x dia
Circumference
37.5’ =
Diameter = constant point = π 37’30” = 37.5’ 60
37.5
= 2π
22r (where r is radius of the circle)
37.5’ =
π
=
60
Circumference = π x dia 7 22 50 37’30” = 50.625 = 0.625 0
0
0
π
= 2πr (where r is radius of the circle) 37.5’ = 37.5 = 0.625 0 0
=
0
7 77 50 37’30” = 50.625 59
60
22
π = 50 37’30” = 50.625 0 59
0
7
59