Let with . Which statement is true about the curvature of this…

MATHEMATICS · Single correct · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions

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.