How can one get the change in rotation needed to look at a specific position? I could create a rather extensive script using every possible bit of (co)sine rule to get what I need, but I though there would be an easier solution.
Wikipedia, scroll down.
There are lots of functions in Unity which are designed so that you rarely need to deal with the guts of rotation math yourself, and you can often get away without needing to even touch Euler angles too.
For GameObjects, you can use Transform.LookAt
If you're creating a new rotation, you can use Quaternion.LookRotation or Quaternion.Euler
For measuring angles, there's Vector3.Angle
And there are many more helper functions in both the Quaternion class and the Vector3 class. Have a browse through them all first before deciding that you need to deal with Sin, Cos or anything else like that manually!
If you really need to compute an angle yourself, there's always Mathf.Atan2 - see the example provided there.