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Degrees to Radians
Theory & Practice Questions
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: 1 degrees = π/180 radians
Radians and Degrees
π^c = 180°
where π^c = π radians
Relationship between radian measure and degrees
Circumference of the circle with radius 1 unit is given by:
C = 2πr
= 2π(1)
= 2π
T
The arc length of the whole circle is 2π.
∴ There are 2π radians in a whole circle.
But there are 360° in a whole circle (angle of revolution).
So 2π^c = 360°
π^c = 180°
Degrees To Radians
To change from degrees to radians: multiply by π/180
Note: Special measure you will use regularly include –
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Practice Question
- Convert 150° into radians.
Solution
- To convert degrees into radians:
Therefore:
150°=150 x π/180 radians
=150π/180 radians
=5π/6 radians
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