B Measurements of angles in circular method

[parshyaa]

• Why θ in radian equals arc/radius?

I know that it can't be proved but there must be a explanation for this formula. How founder may have got this idea.

 

[Mark44]

• Why θ in radian equals arc/radius?

I know that it can't be proved but there must be a explanation for this formula. How founder may have got this idea.

It's a definition. Definitions aren't proved.
One radian is the angle subtended by a sector of a circle for which the arc length of the sector is equal to the radius of the circle.

 

[parshyaa]

It's a definition. Definitions aren't proved.
One radian is the angle subtended by a sector of a circle for which the arc length of the sector is equal to the radius of the circle.

OK, 2πr/1 = 360°, can we say that here arc = 2πr and radius =1 , therefore we get 2π = 360° , this may be the reason which made founder to make it as a definition , this is just my thinking

 

[Stephen Tashi]

OK, 2πr/1 = 360°, can we say that here arc = 2πr and radius =1 , therefore we get 2π = 360° , this may be the reason which made founder to make it as a definition , this is just my thinking

A major motivation for defining "radian" (in the standard way) is that it makes many mathematical formulas simple. If "radian" were defined differently, then many formulas that effectively have the constant factor of "1" in them would have to be rewritten with a different constant factor.

Are you familiar with the definitions of "angular velocity" and "tangential velocity" as applied to an object moving in a circle ? The definition of "radian" creates a simple relation between them.

If you have studied calculus, you can understand that the definition of "radian" creates a simple relation between trigonometric functions (like sin(x)) and their derivatives.