Sketch the level curves for $\displaystyle z = arctan(x^2 + y^2)$. What does the graph of the function look like?

Attempt:

Let x = k:

1.$\displaystyle z = arctan(k^2 + y^2)$

Let y = k:

2.$\displaystyle z = arctan(x^2 + k^2)$

Let z = k:

3.$\displaystyle k = arctan(x^2 + y^2)$

Now what I am not sure of is how would you draw 1-3? Would you have to use all the steps for curve sketching e.g. first derivative, second derivative etc?