= Solution
The periodic extension is an <even> <triangular wave>: peaks of height one occur at the even integers $x=2k$ and valleys of height zero at the odd integers $x=2k+1$. Adjacent peaks and valleys are joined by straight segments of slopes $\pm1$. The function is continuous and has corners at every integer.
\Image[/past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2005/paper-1-triangular-wave.png]
{title=Period-two triangular wave and its first odd cosine harmonics}
{description=Original graph of the periodic extension of $1-|x|$, together with the first one and four nonconstant terms of its Fourier cosine series.}
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