sin x = 2

In elementary school/kindergarten, I was told you couldn't do 2-5, because you can't take 5 apples if you only have 2. Then they taught us negative numbers.
Next came roots. Can't take a square root of -100, they say, because no number can multiply by itself to make a negative. Then they taught us about i.
Can't divide by 0, they tell us. Now calc is covering limits and cheating the rule with derivatives and such.

I've been told you can't arcsin 2, because sin can only go from -1 to 1, and I want to know if there's any more rule-breaking high level math that deals with this... Is there?
Does some higher leveled math course for collage math nerds let you input a value into sin, and get 2? I've lost a certain degree of trust in the education system when they tell you "it can't be done".

my 2nd grade teacher got PISSED when I brought up negative numbers. She was all "shut up you're gonna confuse the other kids" and I'm thinking "what's confusing about negative?"

I noticed that too though, math is taught to you as a bunch of lies. They like to say "YOU ABSOLUTELY CANNOT DO THIS EVER!" then next year they go "Sorry, we lied. you can do it and now you have to learn it!" I understand that they're trying to simplify things but I wish they wouldn't say something is impossible when they know damn well it is. I'd even accept "You'll learn about that next year" but nooooo.