Mathematics

Problem

Let a circle have radius

r

. An arc of length

r

subtends an angle of

1

radian at the centre. a. (i) Explain, on the basis of proportional reasoning, why an arc of length

a r

subtends an angle of

a

radians, where

a

is any positive real number. b. (ii) Illustrate your explanation by determining the angle subtended at the centre when

a=\dfrac{3}{2}

. Express the result in radians only.