Mathematics

Problem

A classmate attempts to derive the relation

s = r\theta

and writes:\nStep 1: For a special case, when

s = r

, the subtended angle is

1\,\text{rad}

.\nStep 2: Therefore, in general,

\theta = \dfrac{s}{\boxed{\phantom{r}}}

.\nWhich quantity should fill the blank box to complete the derivation correctly? a)

2\pi r

r

r^{2}

s