Mathematics

Problem

A cycloid is generated by

x=t-\sin t

and

y=1-\cos t

for

t>0

. The tangent line at

t=\pi/3

is perpendicular to the tangent line at which of the following parameter values in the interval

\pi < t < 2\pi

? a)

3\pi/2

\pi

4\pi/3

5\pi/3