Mathematics

Problem

For

0\le t\le2\pi

, the curve

x=\sin t,\;y=t-\sin t

is traced once. At which point(s) on the curve is the tangent horizontal? a)

(0,0)

only b) The curve has no horizontal tangent on the given interval c)

(1,\,\dfrac{\pi}{2}-1)

and

(-1,\,\dfrac{3\pi}{2}+1)

(0,0)

and

(0,2\pi)