The PHP Core and its library of extensions contains other, less commonly used or less frequently available API calls than those listed here. If you need a bit of functionality that's already being performed by a core function or some extension, refer to its header files and see if it's not also exported to internals-space for use by extensions or embed wrappers like your project.
Appendix D, "Additional Resources," will highlight just these types of "How'd they do that?" approaches to learning by example. First though, you'll take a look at a set of boiler plate templates for doing the most common tasks that you can freely modify and use in your own projects.