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Workshop  Calculation  &  Science  -  Electronics  Mechanic  Exercise 1.6.25
             WORKSHOP CALCULATION & SCIENCE - CITS
 Trigonometry - Measurement of angles

 Workshop  Calculation  &  Science  -  Electronics  Mechanic  Exercise 1.6.25
 Workshop        Circumference makes an angle (2pr) = 360°
                                              Exercise 1.6.25
 Introduction:Calculation  &  Science  -  Electronics  Mechanic
                        Circumference makes an angle (2πr) = 360°
 Trigonometry - Measurement of angles
 Trigonometry is the branch of mathematics which deals
                 Radius of the circle makes an angle (r) = 1 Radian
 Trigonometry - Measurement of angles      Radius of the circle makes an angle (r) = 1 Radian
 with the study of measurement and relationship of the
 Introduction:         Circumference makes an angle  o
                                             360(2πr) = 360°
 three sides and three angles of a triangle.
                                     C
 Introduction:        Circumference makes an angle (2πr) = 360°
                                        ie :
                                         =
 Trigonometry is the branch of mathematics which deals      Radius of the circle makes an angle (r) = 1 Radian
                                            1Radian
                                      r
 Units:
 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
 with the study of measurement and relationship of the  C  r    360 o  o
 Measurement of Angles
 three sides and three angles of a triangle.
                                    2π
                                             360 o
                                           360
 three sides and three angles of a triangle.                      ie :    C  =   =  1Radian
 There are three systems of measuring the angle:
 Units:                               ie :     r  r =    1Radian
 Units:                            r     1Radian
 (i) Sexagesimal System
 Measurement of Angles            2π r     360 o  o
 Measurement of Angles           2π r     360 360
                                             o
                                       =
 This is called British System.  In this system, one right
 There are three systems of measuring the angle:  r  2π =   1Radian
                                            1Radian
 There are three systems of measuring the angle:  r  =  1Radian
 angle is divided into 90 equal parts which are called
 (i) Sexagesimal System
 degrees.Each part is divided into 60 parts which are called
                                           360
 (i) Sexagesimal System       2π  Radian =  360° o
 minutes.Each minute is divided into 60 parts which are
 This is called British System.  In this system, one right  2π =    360 o
                                          1Radian
 This is called British System.  In this system, one right  π Radian = 180°
 called seconds.The parts so divided respectively are called:
 angle is divided into 90 equal parts which are called
                                  2π =
                                         1Radian
 angle is divided into 90 equal parts which are called  2π  Radian =  360°  o
 degrees.Each part is divided into 60 parts which are called
 One degree (1°), one minute (1') and one second (1")
                                           180
 degrees.Each part is divided into 60 parts which are called  2π  Radian =  360°
 minutes.Each minute is divided into 60 parts which are
                                1 Radian =
 minutes.Each minute is   = 90° (90 degrees)  π Radian = 180° π
 It means 1 right angledivided into 60 parts which are
 called seconds.The parts so divided respectively are called:
 called seconds.The parts so divided respectively are called:  π Radian = 180°
                1 degree (1°) = 60' (60 minutes)
                                            π o
 One degree (1°), one minute (1') and one second (1")  180
                                     1° =  o
 One degree (1°), one minute (1') and one second (1")  1 Radian =    180 o   Radian
                                         180
                1 minute (1') = 60" (60 seconds)
 = 90° (90 degrees)
 It means 1 right angle
                                           π
 It means 1 right angle  = 90° (90 degrees)  Examples 1 Radian =    π
 In Trigonometry, mostly this system is used.
                1 degree (1°) = 60' (60 minutes)
                                          π
                                    1° =
                1 degree (1°) = 60' (60 minutes)  Examples 1 Convert 45°36’20” into degree and decimal of degree.
                                         π o   Radian
 (ii)  Centesimal System
                1 minute (1') = 60" (60 seconds)
                                         180
                                   1° =
                                           o   Radian
                1 minute (1') = 60" (60 seconds)  Examples  60 second = 1 minute
                                        180
 This is called French System.  In this system, the right
 In Trigonometry, mostly this system is used.  1  Convert 45°36’20” into degree and decimal of degree.
                  Examples
 In Trigonometry, mostly this system is used.  1 Convert 45°36’20” into degree and decimal of degree.
 angle is divided into 100 equal parts which are called
                                           20
 (ii)  Centesimal System      20 second =       = 0.333’
 grades.  Each grade is divided into 100 minutes and each 1 Convert 45°36’20” into degree and decimal of degree.
 (ii)  Centesimal System     60 second = 1 minute
                                           60
 minute is divided into 100 seconds.
 This is called French System.  In this system, the right  60 second = 1 minute
 This is called French System.  In this system, the right  60 minute = 1 degree
 angle is divided into 100 equal parts which are called
                                          20
 Parts so divided are respectively called:
 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
                                           36.333
                            20 second =  60
 grades.  Each grade is divided into 100 minutes and each  36.333 minute =    = 0.333’
 One grade (1 g), one minute (1' ), one second (1").
 minute is divided into 100 seconds.
                                                   = 0.606°
                                         60
                                             60e
 minute is divided into 100 seconds.  60 minute = 1 degre
 It means 1 right angle = 100 grades (100g)
 Parts so divided are respectively called:  60 minute = 1 degree
 Parts so divided are respectively called:  45 36’20” = 45.606°
                                          36.333
                                 0
                1 grade (1 g) = 100 minutes (100’)
 One grade (1 g), one minute (1' ), one second (1").  36.333 minute =  36.333   = 0.606°
 One grade (1 g), one minute (1' ), one second (1").  2 Convert 24.59° into degree, minute and second
                                            60
                        36.333 minute =
                                                 = 0.606°
                1 minute (1') = 100 seconds (100")
 It means 1 right angle = 100 grades (100g)
                                           60
 It means 1 right angle = 100 grades (100g)  45 36’20” = 45.606°
                             90° = 100g (because each is a right
                                0
                                1 degree =   60 minute
                1 grade (1 g) = 100 minutes (100’)
                             45 36’20” = 45.606°
                               0
                1 grade (1 g) = 100 minutes (100’) angle)  2 Convert 24.59° into degree, minute and second
                1 minute (1') = 100 seconds (100")
                             0.59 degree =   0.59 x 60   = 35.4’
 This system is easier than Sexagesimal System.  But to 2 Convert 24.59° into degree, minute and second
                1 minute (1') = 100 seconds (100")  2  Convert 24.59° into degree, minute and second
                                1 minute =   60 second
                             90° = 100g (because each is a right
                              1 degree =   60 minute
 use this system many other systems will have to be devised
                             90° = 100g (because each is a right  1 degree =   60 minute
  angle)
                                       =   60 minute
 that is why this system is not used.  angle)     1 degree   0.59 degree =   0.59 x 60   = 35.4’
                              0.4 minute =   60 sec  x   0.4
 This system is easier than Sexagesimal System.  But to  0.59 degree =   0.59 x 60   = 35.4’
 (iii)   Circular System
                                       =   0.59 x 60   = 35.4’

                                         =  24”
 This system is easier than Sexagesimal System.  But to 0.59 degree   1 minute =   60 second
 use this system many other systems will have to be devised
                             1 minute =   60 second
 use this system many other systems will have to be devised 1 minute   Therefore 24.59° =  24 35’24”

                                       =   60 second
 In this system, the unit of measuring angles is radian.  It
 that is why this system is not used.
                                             0
                            0.4 minute =   60 sec  x   0.4
 that is why this system is not used.  0.4 minute =   60 sec  x   0.4
 is that angle which is formed at the centre and is formed
 (iii)   Circular System     0.4 minute   =   60 sec  x   0.4
                                       =  24”
 of an arc of length equal to radius in a circle.
                                 0
 (iii)   Circular System  3 Change 50 37’30” into degrees
                                      =  24”

 In this system, the unit of measuring angles is radian.  It    Therefore 24.59° =  24 35’24”
                                       =  24” 0
 There is one constant ratio between the circumference
                       By changing angle degrees into decimals
 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

 and dia of a circle.  This is represented by  π .
                                           30
 is that angle which is formed at the centre and is formed Therefore 24.59°   0  =  24°35’24”
                   3 Change 50 37’30” into degrees
 of an arc of length equal to radius in a circle.
                                      30” =
 of an arc of length equal to radius in a circle.  3  Change 50°37’30” into degrees  60  = 0.50’
                  3 Change 50 37’30” into degrees
 Circumfere
                              0
 nce
 There is one constant ratio between the circumference  By changing angle degrees into decimals
 = constant point  =  π
 Diameter
 There is one constant ratio between the circumference By changing angle degrees into decimals
                     By changing angle degrees into decimals
 and dia of a circle.  This is represented by  π .
                                  37’30” = 37.5’
                                          30
 and dia of a circle.  This is represented by  π .      30” =   30  = 0.50’
 = π x dia
 Circumference
 Circumfere      30”               30”  = =    60  = 0.50’
 nce
                                            = 0.50’
 nce
 Circumfere      = constant point  =  π  37.5’ =  37.5   = 0.625 0
 = 2πr (where r is radius of the circle)
                                         60
 Diameter
                                            60
 Diameter  = constant point  =  π     37’30”   37’30” = 37.5’
 22
                                       = 37.5’
 Circumference  π  = π x dia   37’30” = 37.5’
 =
                                 0
 Circumference  = π x dia      50 37’30” = 50.625 0
                                         37.5
 7
 = 2πr (where r is radius of the circle)
                                 37.5’ =
 = 2πr (where r is radius of the circle)  37.5’ =  37.5   = 0.625 0  59
                                          60
                                              = 0.625
                                                    0
 22
                                         60
 π  =   22                    50 37’30” = 50.625 0
                                0
 π  =    7                   50 37’30” = 50.625 0          78
                               0
 7                                                               59
                                            CITS : WCS - Electrical - Exercise 7
                                                                59
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