How to securely connect to a web api from a Angula

Being relatively new to web development, at least using client side technologies such as the AngularJS framework, I need to resolve a few queries before I can start my latest project.

I am writing an application using the AngularJS which reads/writes/updates data in a database. With javascript being client side I have chosen to write a PHP REST API to do the database queries, resulting in a secure username and password and a single database layer.

My question is, given my REST API, I will be using AJAX from javascript (which is client side) to invoke methods. How do I stop other sites from writing a script to invoke the REST API as well? Putting an authentication token in the javascript code isn't very secure, someone can just copy it.

Is a REST API the best approach for this problem? I am not adverse to learning new technologies or practices so please, any thoughts on better design patterns or methods of implementation are greatly appreciated. Unfortunately, due to my limited domain knowledge in this area, I have been unfruitful in my Google Searches as I'm not confident of the terms under which I should be searching.

Many thanks.

Since your Angular application is living in the browser, your REST API will need to be publicly accessible from any random visitor's browser. You thereby have a public API, out of necessity. You can't restrict it; either visitors can see the data or they can't.

Essentially this is not significantly different from a traditional webpage though. In a server-side generated page, you output your data packaged as HTML and deliver it to anyone who asks. In a REST-API/Angular app, you deliver the data packaged as JSON to anyone who asks. Either way the data is equally public, though maybe the REST API is a little easier to "abuse" than scraping the HTML would be. It may be useful to deliberate employing some user behaviour tracking and throttling, if you want to avoid someone outright sucking all of your database dry; this applies equally to JSON based REST APIs as it does to regular web pages.

If you're also exposing read/write APIs this way, you're of course wide open to abuse.

The only way to make an API non-public is to require password authentication. If the users of your site must be logged in, then you can restrict the API to anyone with a valid session. This doesn't help much in the grant scheme of things if anyone can simply register an account on your site, but it needs more deliberation and provides slightly more manageability than a completely open API.

Admin-only APIs of course must be protected in this way, requiring an account which only you have the credentials to.