  Motivated by the recent prediction of anisotropy in piezoresistance of
ballistic graphene along longitudinal and transverse directions, we investigate
the angular gauge factor of graphene in the ballistic and diffusive regimes
using highly efficient quantum transport models. It is shown that the angular
guage factor in both ballistic and diffusive graphene between $0^{\circ}$ to
$90^{\circ}$ bears a sinusoidal relation with a periodicity of $\pi$ due to the
reduction of six-fold symmetry into a two-fold symmetry as a result of applied
strain. The angular gauge factor is zero at critical angles $20^{\circ}$ and
$56^{\circ}$ in ballistic and diffusive regimes respectively. Based on these
findings, we propose a graphene based ballistic nano-sensor which can be used
as a reference piezoresistor in a Wheatstone bridge read-out technique. The
reference sensors proposed here are unsusceptible to inherent residual strain
present in strain sensors and unwanted strain generated by the vapours in
explosives detection. The theoretical models developed in this paper can be
applied to explore similar applications in other 2D-Dirac materials. The
proposals made here potentially pave the way for implementation of NEMS strain
sensors based on the principle of ballistic transport, which will eventually
replace MEMS piezoresistance sensors with a decrease in feature size. The
presence of strain insenstive ``critical angle'' in graphene may be useful in
flexible wearable electronics also.
