Mathematics

Problem

Consider the curve

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

for

0\le t<2\pi

. At which value(s) of

t

does the curve have a vertical tangent? a)

t=\dfrac{\pi}{2}

only b)

t=\dfrac{\pi}{2}

and

t=\dfrac{3\pi}{2}

t=\dfrac{3\pi}{2}

only d) The curve has no vertical tangent in the given interval