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We study the Josephson effect in spin-singlet superconductor/helical $p$-wavesuperconductor junctions with a ferromagnetic barrier using the quasiclassicalGreen function method. It is found that both $\sin{\phi}$-type and$\cos{\phi}$-type current-phase relations always exist, irrespective of the gapsymmetries in superconductors. The indispensable condition for the$\sin{\phi}$-type and $\cos{\phi}$-type current is that the magnetization musthave a component parallel to the crystallographic $a$ or $b$ axis, which isdistinct from the case of $p$-wave superconductor described by a$\vect{d}$-vector with a uniform direction. The relation between the conditionand the symmetries of the gap functions is analysed. We investigate in detailthe symmetries and the sign reversal of the Josephson current when themagnetization is rotated.

Josephson effect in spin-singlet superconductor/ferromagnetic insulator/spin-triplet superconductor junctions with helical $p$-wave states