Respuesta :
A unit circle has radius 1, and thus circumference [tex]2\pi[/tex].
Since an angle of [tex]\frac{\pi}{4}[/tex] is one eighth of a whole turn, the length of an arc that subtends an angle of [tex]\frac{\pi}{4}[/tex] radians will be one eighth of the whole circumference:
[tex]l = \dfrac{2\pi}{8} = \frac{\pi}{4}[/tex]
In fact, the radians have the property that, in the unit circle, the length of the arc is exactly the measure of the angle. In general, you have
[tex]l = r\cdot\alpha[/tex]
where l is the length of the arc, r is the radius and [tex]\alpha[/tex] is the angle in radians. So, if [tex]r=1[/tex], you have [tex]l=\alpha[/tex]
