= Solution
The <curve> starts at $y(0)=-\sqrt3$ and initially rises. It crosses zero at $x=\pi/3$ and $4\pi/3$, attains its maximum at \b[$(5\pi/6,2)$] and minimum at \b[$(11\pi/6,-2)$], then returns to $y(2\pi)=-\sqrt3$. These follow either from the shifted <sine> form or from $y'=2\cos(x-\pi/3)$.
\Image[/past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2011/paper-1-periodic-response.png]
{title=The unique periodic sinusoidal response, with its maximum, minimum and zero crossings}
Back to article page
