Question

the radius of a circle is 1 what is the length of an arc that subtends an angle of pi/4 radians.

Answer 1

In order to calculate the length of this arc, we can use a rule of three, knowing that the complete circle has an angle of 2π and a length of 2πr:

$\begin{gathered} \text{angle }\to length \\ 2\pi\to2\pi r \\ \frac{\pi}{4}\to x \\ \\ x\cdot2\pi=\frac{\pi}{4}\cdot2\pi r \\ x=\frac{\pi}{4}\cdot r \\ x=\frac{\pi}{4} \end{gathered}$

So the length of the arc is π/4.