Finding the angle of inclination of a cone. After my lecture on solving triple integrals with spherical coordinates, we defined $\phi$ as the angle of inclination from the positive z-axis such that $0\leq \phi \leq\pi$.
What I don't understand is given an equation of a cone:
$$z= c \, \sqrt{x^2+y^2}$$ 
for some constant c, why is:
$$\phi = \arctan \left (\frac{1}{c} \right )$$
Our professor just did not justify this.
Thanks!

$ z = c\, r $ is the generator of cone slanting side, apex at origin.
slope of cone generator = $$ \dfrac {dr}{dz} =\tan \phi =\dfrac{1}{c}. $$
