  High-precision space observations, such as made by the \kepler\ and \corot\
missions, allow us to detect mixed modes for $l = 1$ modes in their high
signal-to-noise photometry data. By means of asteroseismology, the inner
structure of red giant (RG) stars is revealed the first time with the help of
mixed modes. We analyse these mixed modes of a 1.3 M$_{\sun}$ RG model
theoretically from the approximate asymptotic descriptions of oscillations.
While fitting observed frequencies with the eigenvalue condition for mixed
modes, a good estimate of period spacing and coupling strength is also acquired
for more evolved models. We show that the behaviour of the mode inertia in a
given mode varies dramatically when the coupling is strong. An approximation of
period spacings is also obtained from the asymptotic dispersion relation, which
provides a good estimate of the coupling strength as well as period spacing
when g-mode-like mixed modes are sufficiently dense. By comparing the
theoretical coupling strength from the integral expression with the ones from
fitting methods, we confirmed that the theoretical asymptotic equation is
problematic in the evanescent region due to the potential singularities as well
as the use of the Cowling approximation.
