Is this a bad way of approaching math problems? Teacher assigns a problem.  I work on it for thirty minutes, then check the textbook to see if it has similar problems.  Often the textbook's problems have hints that I can use to solve the original problem.
Is this cheating (or otherwise a bad way of solving problems)?
 A: There isn't really such a thing as cheating in solving math problems, but there's such a thing as cheating in courses, and those are two different things.
What you describe is not cheating unless there are constraints you haven't told us about (e.g. it's during a closed-book exam).
In a perfect world, or in a better world, there would be more emphasis on solving problems that you haven't been told how to solve.  I.e. you'd have been given enough information to figure it out if you put your brain in gear, but instead of resembling problems you've seen in the book, it might simply be a problem that relies on understanding of concepts you've seen in the book.  In that case, you'd still want to look at the book.
A: It's not cheating: it's learning. You solve the problem with the help of a kind of teacher (here the book is the teacher). It's a good way to learn something you dont know (here that the problem has connections with others, and how to solve them). 
You are not supposed to know everything when you do your homework, but you are supposed to do your best to understand and learn. Which is what you are doing, I guess. 
