sphere coordinates and trigonometry

three parameters: (r, θ, φ)
$x = r cdot sin(φ) cos(θ)$
$y = r cdot sin(φ) sin(θ)$
$z = r cdot cos(θ)$

$cos(θ) = frac{x}{sqrt{x^{2} + y^{2}}}$
$sin(θ) = frac{y}{sqrt{x^{2} + y^{2}}}$
$tan(θ) = frac{y}{x}$

arcsin/arccos/arctan is the inverse.
e.g.
$tan(45^{circ}) = 1$
$arctan(1) = 45^{circ}$