What is a radian?

• Sep 20th 2009, 08:52 AM
algebraisabeast
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?
• Sep 20th 2009, 09:08 AM
Plato
Quote:

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.

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 $\displaystyle (1.5)(10)$.
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 $\displaystyle 2\pi$ radians will subtend an arc of $\displaystyle 20\pi$ units the whole circle.