Maple: How to convert Cylindrical coordinates to Cartesian coordinates?

Simplify(toCyl) assuming r>=0, `ϕ`-Pi; Notice, arctan(sin(Pi/4),cos(Pi/4)); 1 - Pi 4 arctan(sin(Pi/4 + 10*Pi),cos(Pi/4 + 10*Pi)); 1 - Pi 4 arctan(sin(-7*Pi/4),cos(-7*Pi/4)); 1 - Pi 4 arctan(sin(-15*Pi/4),cos(-15*Pi/4)); 1 - Pi 4 arctan(sin(-Pi),cos(-Pi)); Pi K:=arctan(r*sin(Pi/4),r*cos(Pi/4)); arctan(r, r) simplify(K) assuming r0; 1 - Pi 4 Once you've converted from cylindrical to rectangular, any information about how many times the original angle" might have wrapped around (past -Pi) is lost. So you won't recover the original ϕ unless it was in (-Pi,Pi. If you tell Maple that is the case (along with r>-0 so that it knows which half-plane), using assumptions, then it can simplify to what you're expecting.

So... top line still gives me arctan(sin(ϕ), cos(ϕ)) please see post update. – Blender May 18 at 17:21 It works for me, provided that the mentioned assumption is supplied. – acer Jun 3 at 13:41.

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