Date: 5/31/2014 3:11 PM UTC
The short answer is never. That's not a typo: you will almost certainly never use the Pythagorean Theorem or the Quadratic Formula or SOH CAH TOA ever again once you're finished with school. These things just don't come up in everyday life, nor in at least 99% of the jobs out there. Unless you go on to become a mathematician or a teacher, you can probably forget these specific bits of knowledge, as well as how to use them, on the day you graduate, and you won't ever suffer a bit for it.
Here's the longer answer: it depends on what you mean by “this.” If you're talking about the particular things you're studying right now in math class, or almost any other class for that matter, you can stick with the answer above. You're probably never going to use it. What you are going to use though, no matter what you do with the rest of your life, is your brain. Your brain is an incredibly complex machine that allows you to do one thing far better than any other animal in the world: solve problems. You aren't born knowing how to do this though. It takes practice! When you work through a math problem from start to finish, what you are really doing is training your brain to solve problems logically. This creates powerful, lasting connections between your brain cells that allow you to apply this type of reasoning to all sorts of problems, whether they involve numbers or not! Math isn't really teaching you how to calculate the circumference of a circle. It's actually training you to find the answers to the many questions you face daily.
Think about an athlete who stretches every day. She might think to herself one morning, “When will I ever need to bend down and touch my toes?” She won't, of course! There's no Toe-Touching event in the Olympics! So why does she do this day after day? It's because she will use the flexibility she gains from doing this to perform a lot of the actions she needs to as part of her sport.
Think about that the next time you're in class and somebody asks, “When am I ever going to use this?” Now you can say, “Your brain? Every day for the rest of your life!”