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I'm fairly new to Mathematica, and I'm trying to solve a complicated equation with multiple variables. I've tried the following...

Reduce[-2 (m^2/36 + n^2/4)^(1/4) Sin[1/2 ArcTan[n/2, -(m/6)]] == y, {n}]

Where I would like to have n on one side of the equation, defined by m and y. Is this the correct notation and I just need to wait longer for the equation to solve? Or am I making a mistake somewhere?

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I'd only be able to use an analytical solution for the next part of my problem. So if an equation is too complicated for Mathematica will it say so? Or just never output an answer? – Tait Jul 29 '14 at 7:20
up vote 6 down vote accepted

Many times I've found Mathematica to be way better solving equations, when trigonometric functions are written with exponential functions. This time is no exception:

Solve[FullSimplify[TrigToExp[-2 (m^2/36 + n^2/4)^(1/4) Sin[1/2 ArcTan[n/2,-(m/6)]]==y]],n]
{{n -> (m^2 - 9 y^4)/(18 y^2)}}
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Wow that is awesome, thank you for the answer! – Tait Jul 29 '14 at 7:58

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