# How to calculate the solid angle of a cone with cone axis arbitrary?

by soljiang
Tags: angle, arbitrary, axis, cone, solid
 P: 6 I read that if the cone with apex angle 2α whose central axis is vertical, apex at the origin, then one can use spherical coordinate to calculate the solid angle of the cone ∫02∏∫0αsin$\varphi$d$\theta$d$\varphi$ However, what if the central axis is align to y-axis horizontally, instead of z-axis. My question is with angle 2α, if the central axis goes through (θ0, $\varphi$0), then how to set the intragation boundaries? It should give the same answer but I need to now how to set up the equation. Can one still use spherical coordinate? Thank you so much if I get some help. Best, Charles