ArcTan[3, -3] (* out: *) -Pi/4 ArcTan[3 a Sin[t/2], -3 a Sin[t/2]] (* out: *) ArcTan[3 a Sin[t/2], -3 a Sin[t/2]]
However, we can fix the second one with some assumptions (where applicable)
$Assumptions = a > 0 && Pi > t > 0 Refine@ArcTan[3 a Sin[t/2], -3 a Sin[t/2]] (* out: *) -Pi/4
I need a way to force mathematica to similarly realize it can cancel units in the ArcTan (which is basically a ratio, except for the sign consideration for the quadrant).
For example, say I now have
$Assumptions = a > 0 && Pi > t > 0 aa=(4 Pi/(3 Sqrt))(Quantity[1.42, "Angstroms"])^(-1) b=(Quantity[5, "Angstroms"])^(-1) ArcTan[b+3 aa Sin[t/2],-b-3 aa Sin[t/2]]
How can I force Mathematica to recognize that these arguments are just +c and -c and thus the ArcTan significantly reduces?
I wish to avoid removing the units here artificially with QuantityMagnitude because elswhere in these expressions the units appear outside of these ArcTans. However, a last ditch solution would be one that simply searched for these ArcTan and applied QuantityMagnitude to their arguments, I suppose.