What is a radian?

What is a radian? A radian is the measure of an angle at the centre of a circle subtended by an arc, whose arc length is equal to the radius of the circle: Not exactly what this means.

When I am looking for arc length I can find the circumference around the circle then take the fraction of the angle that I am given to the whole circle.

If I use the formula S=(thata)r
thata has to be in terms of radians-- why?

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Originally Posted by algebraisabeast

What is a radian? A radian is the measure of an angle at the centre of a circle subtended by an arc, whose arc length is equal to the radius of the circle: Not exactly what this means.

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If you do not know what a centeral angle of a circle, then you must start there.

In a circle of radius 10, any centeral angle of 1.5 radians will subtend an arc of 15 units.
That is .
A centeral angle of 1 radian will subtend an arc of 10 units.
A centeral angle of 3 radians will subtend an arc of 30 units.
A centeral angle of radians will subtend an arc of units the whole circle.