How to use the geographiclib.geodesic.Geodesic._SinCosSeries function in geographiclib

AB2 = (1 + self._A2m1) * (B22 - self._B21)
      J12 = (self._A1m1 - self._A2m1) * sig12 + (AB1 - AB2)
      if outmask & Geodesic.REDUCEDLENGTH:
        # Add parens around (_csig1 * ssig2) and (_ssig1 * csig2) to ensure
        # accurate cancellation in the case of coincident points.
        m12 = self._b * ((      dn2 * (self._csig1 * ssig2) -
                          self._dn1 * (self._ssig1 * csig2))
                         - self._csig1 * csig2 * J12)
      if outmask & Geodesic.GEODESICSCALE:
        t = (self._k2 * (ssig2 - self._ssig1) *
             (ssig2 + self._ssig1) / (self._dn1 + dn2))
        M12 = csig12 + (t * ssig2 - csig2 * J12) * self._ssig1 / self._dn1
        M21 = csig12 - (t * self._ssig1 - self._csig1 * J12) * ssig2 / dn2

    if outmask & Geodesic.AREA:
      B42 = Geodesic._SinCosSeries(False, ssig2, csig2, self._C4a)
      # real salp12, calp12
      if self._calp0 == 0 or self._salp0 == 0:
        # alp12 = alp2 - alp1, used in atan2 so no need to normalize
        salp12 = salp2 * self.calp1 - calp2 * self.salp1
        calp12 = calp2 * self.calp1 + salp2 * self.salp1
      else:
        # tan(alp) = tan(alp0) * sec(sig)
        # tan(alp2-alp1) = (tan(alp2) -tan(alp1)) / (tan(alp2)*tan(alp1)+1)
        # = calp0 * salp0 * (csig1-csig2) / (salp0^2 + calp0^2 * csig1*csig2)
        # If csig12 > 0, write
        #   csig1 - csig2 = ssig12 * (csig1 * ssig12 / (1 + csig12) + ssig1)
        # else
        #   csig1 - csig2 = csig1 * (1 - csig12) + ssig12 * ssig1
        # No need to normalize
        salp12 = self._calp0 * self._salp0 * (
          self._csig1 * (1 - csig12) + ssig12 * self._ssig1 if csig12 <= 0

AB2 = (1 + self._A2m1) * (B22 - self._B21)
      J12 = (self._A1m1 - self._A2m1) * sig12 + (AB1 - AB2)
      if outmask & Geodesic.REDUCEDLENGTH:
        # Add parens around (_csig1 * ssig2) and (_ssig1 * csig2) to ensure
        # accurate cancellation in the case of coincident points.
        m12 = self._b * ((      dn2 * (self._csig1 * ssig2) -
                          self._dn1 * (self._ssig1 * csig2))
                         - self._csig1 * csig2 * J12)
      if outmask & Geodesic.GEODESICSCALE:
        t = (self._k2 * (ssig2 - self._ssig1) *
             (ssig2 + self._ssig1) / (self._dn1 + dn2))
        M12 = csig12 + (t * ssig2 - csig2 * J12) * self._ssig1 / self._dn1
        M21 = csig12 - (t * self._ssig1 - self._csig1 * J12) * ssig2 / dn2

    if outmask & Geodesic.AREA:
      B42 = Geodesic._SinCosSeries(False, ssig2, csig2, self._C4a)
      # real salp12, calp12
      if self._calp0 == 0 or self._salp0 == 0:
        # alp12 = alp2 - alp1, used in atan2 so no need to normalize
        salp12 = salp2 * self.calp1 - calp2 * self.salp1
        calp12 = calp2 * self.calp1 + salp2 * self.salp1
      else:
        # tan(alp) = tan(alp0) * sec(sig)
        # tan(alp2-alp1) = (tan(alp2) -tan(alp1)) / (tan(alp2)*tan(alp1)+1)
        # = calp0 * salp0 * (csig1-csig2) / (salp0^2 + calp0^2 * csig1*csig2)
        # If csig12 > 0, write
        #   csig1 - csig2 = ssig12 * (csig1 * ssig12 / (1 + csig12) + ssig1)
        # else
        #   csig1 - csig2 = csig1 * (1 - csig12) + ssig12 * ssig1
        # No need to normalize
        salp12 = self._calp0 * self._salp0 * (
          self._csig1 * (1 - csig12) + ssig12 * self._ssig1 if csig12 <= 0

(self.caps & (Geodesic.OUT_MASK & Geodesic.DISTANCE_IN))):
      # Uninitialized or impossible distance calculation requested
      return a12, lat2, lon2, azi2, s12, m12, M12, M21, S12

    # Avoid warning about uninitialized B12.
    B12 = 0.0; AB1 = 0.0
    if arcmode:
      # Interpret s12_a12 as spherical arc length
      sig12 = math.radians(s12_a12)
      ssig12, csig12 = Math.sincosd(s12_a12)
    else:
      # Interpret s12_a12 as distance
      tau12 = s12_a12 / (self._b * (1 + self._A1m1))
      s = math.sin(tau12); c = math.cos(tau12)
      # tau2 = tau1 + tau12
      B12 = - Geodesic._SinCosSeries(True,
                                    self._stau1 * c + self._ctau1 * s,
                                    self._ctau1 * c - self._stau1 * s,
                                    self._C1pa)
      sig12 = tau12 - (B12 - self._B11)
      ssig12 = math.sin(sig12); csig12 = math.cos(sig12)
      if abs(self.f) > 0.01:
        # Reverted distance series is inaccurate for |f| > 1/100, so correct
        # sig12 with 1 Newton iteration.  The following table shows the
        # approximate maximum error for a = WGS_a() and various f relative to
        # GeodesicExact.
        #     erri = the error in the inverse solution (nm)
        #     errd = the error in the direct solution (series only) (nm)
        #     errda = the error in the direct solution (series + 1 Newton) (nm)
        #
        #       f     erri  errd errda
        #     -1/5    12e6 1.2e9  69e6

lam12 = omg12 + self._A3c * (
        sig12 + (Geodesic._SinCosSeries(True, ssig2, csig2, self._C3a)
                 - self._B31))
      lon12 = math.degrees(lam12)
      lon2 = (self.lon1 + lon12 if outmask & Geodesic.LONG_UNROLL else
              Math.AngNormalize(Math.AngNormalize(self.lon1) +
                                Math.AngNormalize(lon12)))

    if outmask & Geodesic.LATITUDE:
      lat2 = Math.atan2d(sbet2, self._f1 * cbet2)

    if outmask & Geodesic.AZIMUTH:
      azi2 = Math.atan2d(salp2, calp2)

    if outmask & (Geodesic.REDUCEDLENGTH | Geodesic.GEODESICSCALE):
      B22 = Geodesic._SinCosSeries(True, ssig2, csig2, self._C2a)
      AB2 = (1 + self._A2m1) * (B22 - self._B21)
      J12 = (self._A1m1 - self._A2m1) * sig12 + (AB1 - AB2)
      if outmask & Geodesic.REDUCEDLENGTH:
        # Add parens around (_csig1 * ssig2) and (_ssig1 * csig2) to ensure
        # accurate cancellation in the case of coincident points.
        m12 = self._b * ((      dn2 * (self._csig1 * ssig2) -
                          self._dn1 * (self._ssig1 * csig2))
                         - self._csig1 * csig2 * J12)
      if outmask & Geodesic.GEODESICSCALE:
        t = (self._k2 * (ssig2 - self._ssig1) *
             (ssig2 + self._ssig1) / (self._dn1 + dn2))
        M12 = csig12 + (t * ssig2 - csig2 * J12) * self._ssig1 / self._dn1
        M21 = csig12 - (t * self._ssig1 - self._csig1 * J12) * ssig2 / dn2

    if outmask & Geodesic.AREA:
      B42 = Geodesic._SinCosSeries(False, ssig2, csig2, self._C4a)

if outmask & Geodesic.LONGITUDE:
      # tan(omg2) = sin(alp0) * tan(sig2)
      somg2 = self._salp0 * ssig2; comg2 = csig2 # No need to normalize
      E = Math.copysign(1, self._salp0)          # East or west going?
      # omg12 = omg2 - omg1
      omg12 = (E * (sig12
                    - (math.atan2(          ssig2,       csig2) -
                       math.atan2(    self._ssig1, self._csig1))
                    + (math.atan2(E *       somg2,       comg2) -
                       math.atan2(E * self._somg1, self._comg1)))
               if outmask & Geodesic.LONG_UNROLL
               else math.atan2(somg2 * self._comg1 - comg2 * self._somg1,
                               comg2 * self._comg1 + somg2 * self._somg1))
      lam12 = omg12 + self._A3c * (
        sig12 + (Geodesic._SinCosSeries(True, ssig2, csig2, self._C3a)
                 - self._B31))
      lon12 = math.degrees(lam12)
      lon2 = (self.lon1 + lon12 if outmask & Geodesic.LONG_UNROLL else
              Math.AngNormalize(Math.AngNormalize(self.lon1) +
                                Math.AngNormalize(lon12)))

    if outmask & Geodesic.LATITUDE:
      lat2 = Math.atan2d(sbet2, self._f1 * cbet2)

    if outmask & Geodesic.AZIMUTH:
      azi2 = Math.atan2d(salp2, calp2)

    if outmask & (Geodesic.REDUCEDLENGTH | Geodesic.GEODESICSCALE):
      B22 = Geodesic._SinCosSeries(True, ssig2, csig2, self._C2a)
      AB2 = (1 + self._A2m1) * (B22 - self._B21)
      J12 = (self._A1m1 - self._A2m1) * sig12 + (AB1 - AB2)

lam12 = omg12 + self._A3c * (
        sig12 + (Geodesic._SinCosSeries(True, ssig2, csig2, self._C3a)
                 - self._B31))
      lon12 = math.degrees(lam12)
      lon2 = (self.lon1 + lon12 if outmask & Geodesic.LONG_UNROLL else
              Math.AngNormalize(Math.AngNormalize(self.lon1) +
                                Math.AngNormalize(lon12)))

    if outmask & Geodesic.LATITUDE:
      lat2 = Math.atan2d(sbet2, self._f1 * cbet2)

    if outmask & Geodesic.AZIMUTH:
      azi2 = Math.atan2d(salp2, calp2)

    if outmask & (Geodesic.REDUCEDLENGTH | Geodesic.GEODESICSCALE):
      B22 = Geodesic._SinCosSeries(True, ssig2, csig2, self._C2a)
      AB2 = (1 + self._A2m1) * (B22 - self._B21)
      J12 = (self._A1m1 - self._A2m1) * sig12 + (AB1 - AB2)
      if outmask & Geodesic.REDUCEDLENGTH:
        # Add parens around (_csig1 * ssig2) and (_ssig1 * csig2) to ensure
        # accurate cancellation in the case of coincident points.
        m12 = self._b * ((      dn2 * (self._csig1 * ssig2) -
                          self._dn1 * (self._ssig1 * csig2))
                         - self._csig1 * csig2 * J12)
      if outmask & Geodesic.GEODESICSCALE:
        t = (self._k2 * (ssig2 - self._ssig1) *
             (ssig2 + self._ssig1) / (self._dn1 + dn2))
        M12 = csig12 + (t * ssig2 - csig2 * J12) * self._ssig1 / self._dn1
        M21 = csig12 - (t * self._ssig1 - self._csig1 * J12) * ssig2 / dn2

    if outmask & Geodesic.AREA:
      B42 = Geodesic._SinCosSeries(False, ssig2, csig2, self._C4a)