0
$\begingroup$

I have an equation: $x = \frac{y}{\tan y}$ or rewritten as: $y = x\tan y$

How can I rearrange this so that I can calculate $y$ given $x$?

1 Answers 1

1

Doing so would involve calculating the inverse of the tanc function,

$y = \operatorname{tanc}^{-1}\frac{1}{x}$

There is no expression for this function in terms of other elementary functions, so you can't find an analytic solution. You could find the solutions of your equation numerically, though, once you're given an explicit numerical value for $x$.

  • 1
    For those who are interested, a lot of information about the situation when $x = 1$ (i.e. numerical solutions to the equation $\tan y = y$) is linked at the following URL, including a .pdf file of the LaTeX slides I used for an Iowa MAA Section talk I gave on this equation (8 April 2006). http://mathforum.org/kb/message.jspa?messageID=70143082012-01-11