Mathematics

Problem

Let

\mathbf r(t)=\langle R\cos t,\,R\sin t,\,0\rangle

with

R>0

. Which statement is true about the curvature

\kappa(t)

of this curve? a)

\kappa(t)=\dfrac{1}{R^{2}}

for all

t

. b)

\kappa(t)=\dfrac{1}{R}

for all

t

. c)

\kappa(t)=\dfrac{|\sin t|}{R}

. d)

\kappa(t)

is not constant because the parameterization is not by arc length.