Some while ago, I covered how to convert degrees into radians (and vice versa) in your head. I missed a trick, though: I didn't tell you about the exact values, which would probably have been a bit more useful.
By definition, a circle -- 360º -- is 2π radians, which (hopefully obviously) means that a semicircle -- 180º, keep up -- is π radians. That's a handy thing to know.
This is the wrong way! As I've said before, degrees are far inferior to radians in every possible application. But still, I imagine you might want to go back to baby-angles once in a while.
You'll quite often see an angle given in radians as some fraction of π -- π/6 or 3π/2 or similar. It's pretty easy to turn those into degrees: if you're good with fractions, just replace the π with 180 and work it out: π/6 becomes 180/6 = 30º. 3π/2 becomes 3 × 180 / 2 = 3 × 90 = 270º1.
If you don't like fractions, I'll sit here and roll my eyes a bit, then tell you that if there's a number on top of the fraction, you times by it; and then you divide by the number on the bottom. Meanwhile, I'll line up a Teletubbies DVD for you or something. You're an A-level student, you need to be able to work with fractions.
Ah, that's better. Turning things into radians is, of course, the way forward. It's a simple three-step process:
And that's it. Of course, it's worth knowing the more common ones off the top of your head:
Thanks to @C_J_Smith for pointing out a mistake in the original version.