SUPPLEMENTARY UNITS AND RADIAN

SUPPLEMENTARY UNITS

DEFINITION
The S.I units which are not yet classified either base or derived unit is known as Supplementary Units
NUMBER
In number these are Two 1) RADIAN
2) STERADIAN

RADIAN
DEFINITION
The unit of plane angle subtended by an arc of length equal to its radius at center of circle is known as radian
SYMBOL
It is denoted by 'rad'
EXPLANATION
Consider a circle whose radius is 'r'.If the length of arc AC is equal to radius 'r' of the given circle then
Now we know from trigonometry that the ratio of angles subtended by arcs is equal to the ratio of the length of arcs i.e Ø =s/r × 1rad ........ eq (1)
When s= r (length of arc=radius of the cicle then equation 1 can be written as
Ø=1 rad
When we are finding radians in one complete circle then put s =2πr (circumference of the circle)
Ø=2πr/r × 1rad
Ø= 2πr rad ..........eq (2) Eq .2 gives us radians in one revolution

OTHER UNIT OF PLANE ANGLE
Degree is another unit of plane angle
One revolution=360 degree.........eq .(3)
1 degree has 60 minutes
1 minute has 60 seconds

RELATION BETWEEN DEGREE AND RADIAN
From eq .2 and eq .3 we conclude that in one complete revolution has 2πr radian and 360 degree so comparing these two equations we have that
2πr rad= 360 degree
1 rad =
1 rad = 57.3 degree