Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2009 / Paper 1 / 8 / b

Write $y=\frac{1}{2}\sin (2x)$. It is an odd function with amplitude $1/2$ and period $\pi$. Its zeros on the specified interval are $-\pi ,-\pi /2,0,\pi /2,\pi$. The maxima are at $x=-3\pi /4,\pi /4$ and the minima at $x=-\pi /4,3\pi /4$, with values $1/2$ and $-1/2$. The middle panel of the preceding figure shows the two full oscillations.