# The “sin-cos-maximum” function

Is there some specific notation for the function

$f(x):=\max\{\cos(x),\sin(x)\}$,

or maybe some equivalent compact expression?

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

$g(x):=\max\{\cos^2(x),\sin^2(x)\}$,

is easier.

A way is: $$f(x)=\left\{ \begin{array}{ll} \cos{x}, & \left[2\pi k-\frac{3\pi}{4},2\pi k+\frac{\pi}{4}\right]\\\\ \sin{x}, & \left[2\pi k+\frac{\pi}{4},2\pi k+\frac{5\pi}{4}\right] \end{array} \right.,\quad \text{with}\quad k\in\mathbb{Z}$$
• @Arkamis In the end points, $\sin{x}=\cos{x}$. – AsdrubalBeltran Dec 16 '14 at 2:31