# How to improve the graph for an implicit function $|\sin x|^y + |\cos x|^y = 1$

I've recently posted a question on Math.SE related to the graph of the following function: $$|\sin x|^y + |\cos x|^y = 1$$

I had some troubles with transforming the function to see what the graph looks like so decide to refer to desmos, W|A and Mathematica neither of which gave me the exact plot. I would like to know:

Is it possible to improve the graph or apply some (general) technique so that it's more accurate than the ones by the link?

Here is a snippet for copy and paste: ContourPlot[Abs[Cos[x]]^y + Abs[Sin[x]]^y == 1, {x, -Pi, Pi}, {y, 0, 3}]

And its output: Please note that i'm fairly new to Mathematica and may miss something that may be obvious for an experienced user.

The refinement of a plot can be achieved with the Option MaxRecursion -> ...
ContourPlot[Abs[Cos[x]]^y + Abs[Sin[x]]^y == 1, {x, -Pi, Pi}, {y, 0, Pi}, MaxRecursion -> 5] • Thank for your answer, you could not reproduce it due to my fault. I was plotting it for $x \in [- \pi , \pi]$. I've just updated the OP – roman Aug 2 '18 at 9:15
• If $x=\frac \pi 2$, then $y$ may be an arbitrary positive real number. The same issue with $x=− \frac \pi 2$ and $x=\pi$ and $x=−\pi$. – user64494 Aug 2 '18 at 11:13