I doubt those critical shared libraries include things like rotation. NEON is probably used to improve performance of things like memcpy and string operations, probably mostly integer stuff.
All geometry in OpenGL will be shaded by multiplying it against a transformation matrix. In OpenGL ES 2.0 you have to do this manually in a vertex shader, while in OpenGL ES 1.x it'll happen for you and will be based on how you setup OpenGL state matrices (projection, modelview). Either way, the actual vertex rotation happens in hardware, but setting up the rotation matrix happens in software (normally anyway, technically you can setup the shaders to do matrix math too, and there's an IMG compiler optimization to get them to not redo it for every vertex, but it has to be done just right). If you're doing a call to standard sin/cos to do this it'll be relatively slow no matter what, but you shouldn't need to constantly create rotation matrices.
The parameters in OpenGL ES can be either floating point or fixed point. So you can send both the vectors and the matrices themselves as fixed point, and it'll be converted to floating point on the chip. You can make sin/cos functions that operate in fixed point too; how much faster than the slow non-NEON floating point implementations will depend on how it's done.
You don't want to use double precision because that'll definitely not be implemented with NEON, and it's slower than single precision even in VFPU. sin/cos will especially be slower as double because more approximation steps will have to be taken in software. You should use single precision (float) instead, and sinf/cosf if you have to.
Since you seem to be starting out with this sort of thing I recommend using OpenGL ES 1.1 first, and using glRotatef to setup the modelview matrix for rotations. If you have to do it yourself check out Adventus's NEON math library - it has matrix multiplication and sin/cos implementations using NEON.
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