Write $y=\tfrac12\sin(2x)$. 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.

Solution

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 / Solution

 Solution (source code)