The "sin-cos-maximum" function

Question

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.

look at what a "robot" can do http://www.wolframalpha.com/input/?i=plot+max%7Bcos+x%2C+sin+x%7D — janmarqz, Dec 16 '14 at 01:58
A useful answer to "equivalent expression" depends largely on the context you intend to use such an expression for. — Milo Brandt, Dec 16 '14 at 02:04

score 1 · Answer 1 · answered Dec 16 '14 at 02:15

1

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

answered Dec 16 '14 at 02:15

AsdrubalBeltran

4,212

2

Well, the intervals are compact. – Emily Dec 16 '14 at 02:26
1

@Arkamis In the end points, $\sin{x}=\cos{x}$. – AsdrubalBeltran Dec 16 '14 at 02:31
I know. I was remarking that the OP wanted a compact expression. This is... decidedly less so ;) – Emily Dec 16 '14 at 02:35

The "sin-cos-maximum" function

1 Answers1