Is there some specific notation for the function


or maybe some equivalent compact expression?

Improvement: Actually, maybe a compact equivalent expression for its squared version


is easier.


A way is: $$f(x)=\left\{ \begin{array}{ll} \cos{x}, & \left[2\pi k-\frac{3\pi}{4},2\pi k+\frac{\pi}{4}\right]\\\\ \sin{x}, & \left[2\pi k+\frac{\pi}{4},2\pi k+\frac{5\pi}{4}\right] \end{array} \right.,\quad \text{with}\quad k\in\mathbb{Z}$$

  • 2
    $\begingroup$ Well, the intervals are compact. $\endgroup$ – Emily Dec 16 '14 at 2:26
  • 1
    $\begingroup$ @Arkamis In the end points, $\sin{x}=\cos{x}$. $\endgroup$ – AsdrubalBeltran Dec 16 '14 at 2:31
  • $\begingroup$ I know. I was remarking that the OP wanted a compact expression. This is... decidedly less so ;) $\endgroup$ – Emily Dec 16 '14 at 2:35

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