A particle moves along the circle for

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

Problem

A particle moves along the circle

x=4\cos t,\;y=4\sin t

for

0\le t\le\pi

. Re-parameterize the motion in terms of arc length

s

measured counter-clockwise from

(4,0)

. Determine

t

as a function of

s

and specify the interval for

s