Mathematics

Problem

The parametric curve

C

is given for

0\le t\le 2\pi

x(t)=2t-\sin t, \qquad y(t)=3-\cos t.

For which value(s) of

t

does

C

have a point of inflection? a)

t=\dfrac{\pi}{2}\;\text{and}\;t=\dfrac{3\pi}{2}

t=\dfrac{\pi}{3}

\; only c)

t=\dfrac{\pi}{3}\;\text{and}\;t=\dfrac{5\pi}{3}

t=\dfrac{2\pi}{3}\;\text{and}\;t=\dfrac{4\pi}{3}