To answer your question simply, there are no set minimum tangent length requirements.
AASHTO does not have any minimum tangent lengths, only minimum lengths of runoff/runout for roads that are superelevated; these runoff/runout distances are generally then considered minimum tangent lengths.
If your road is superelevated, you minimum tangent lengths are driven by the runout/runoff lengths, and a few other design parameters.
If your road is not superelevated, then minimum tangent lengths should be included in your local review agency road design standards - some do not require any at all.
As a designer for numerous low-volume roads, I am usually OK with designing reverse curves with no tangent length, but I do use minimum tangent lengths when designing compound curves ("broken-back") with largely differing radii.
If your new to road design, read Pgs. 229-230 of the PGDHS (2004)(updated "AASHTO Green Book") for some very useful discussion about horizontal road design issues.