Question 741077
A calculator can give you an approximate solution.
If {{{cot(x)=12/13}}}, then {{{tan(x)=1/cot(x)=13/12}}}
and the calculator says that {{{tan^(-1)(13/12)=47.29^o}}} so {{{tan(47.29^o)=13/12}}}
{{{tan(x)}}} is positive and increasing in the first and third quadrant, and has a period of {{{180^o}}} 
The graph below shows {{{y=tan(x)}}} and {{{y=13/12}}}
{{{graph(300,300,-45,405,-5,5,tan(pi*x/180),13/12)}}}
So that {{{tan(47.29^o)=tan(47.29^o+180^o)=tan(227.29^o)}}}
The only two approximate solutions to {{{cot(x)=12/13}}} for {{{0<=x<360^o}}} are
{{{highlight(x=47.29^o)}}} and {{{highlight(x=227.29^o)}}}