The curve and traces a circle of radius for

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

Problem

The curve

x(t)=k\cos t

and

y(t)=k\sin t

traces a circle of radius

k

for

0\le t\le \dfrac{\pi}{2}

. If the length of the curve over this interval is

5

, determine the value of

k