Theory
Radian, a circle measure
One radian is the angle that an arc of 1 unit subtends at the centre of a circle of radius 1 unit.
Degrees to radians conversion:听 1 degrees = 蟺/180 radians
听
Radians and Degrees
蟺^c听= 180掳听
where听蟺^c听听=听蟺听 radians
听
Relationship between radian measure and degrees
Circumference of the circle with radius 1 unit is given by:
C = 2蟺谤
= 2蟺(1)
= 2蟺
T
The arc length of the whole circle is 2蟺.
鈭� There are 2蟺 radians in a whole circle.
But there are 360掳 in a whole circle (angle of revolution).
So 2蟺^c听= 360掳
蟺^c听=听180掳
听
听
Radians to Degrees
To change from radians to degrees:听multiply by 180/蟺
Note: Special measure you will use regularly include -
听
Practice Question
- Convert 5蟺/6 radians听into degrees.
Solution
- To convert radians into degrees:
Therefore:
5蟺/6 radians听=听180/蟺掳 x听5蟺/6
Simplyfying:
=900蟺/6蟺掳
听=150掳
