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".

I'm pretty sure you can't, but I'm only taking Trig right now...

Not as bad as in Elementary when you had to draw each individual little square/rectangle representing a value....

[COLOR="Red"]http://press.princeton.edu/books/maor/chapter_14.pdf

I didn't read all of it, but I think the title answers your question[/COLOR]

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.

Well technically, you really can't divide by 0.

For sin x = 2, you will never have to deal with "imaginary trig" unless you're a math major and doing theoretical stuff. I've taken everything up to Linear Algebra, Calculus with several Variables, and Differential Equations. That's about as far as most people in any Engineering or related majors go.

[COLOR="Red"]http://press.princeton.edu/books/maor/chapter_14.pdf

I didn't read all of it, but I think the title answers your question[/COLOR]

I read through it kinda fast, and didn't see anything really helpful, although the lack of 'sinh' and stuff in my math classes might be part of that....

Well technically, you really can't divide by 0.

For sin x = 2, you will never have to deal with "imaginary trig" unless you're a math major and doing theoretical stuff.

'have to'
I want to. No idea what I'll major in, but I want to play with rule breaking math.

Ah, hyperbolic trig functions.

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.

[COLOR="Red"]Peeking at Patrick's math homework?

I remember doing something similar.

Me: What if you go below zero?
Teacher: You can't do that dear.
Me: Okay...

-One year later-

Teacher: Now we'll be dealing with negatives.

I hate school...[/COLOR]

Sin could be considered as the ratio of one of the sides of a right-angled triangle to the hypotenuse.

The hypotenuse is always the longest side of a right-angled triangle in euclidean space... so it's gotta be less than 1. (a/b where a<b). Euclidean space assumes that parallel lines remain equidistant to infinity, and also leads to this. If parallel lines can meet (imagine the lines on a sphere - 2 great circles are parallel, but meet at a couple points) then the assumption no longer holds. Call this positive curvature for some reason.o.o You can have a triangle with 3 right angles if it's on a sphere, or some other weird stuff where the longest side meets the right angle.

If the top point is at the North pole, and the bottom line is around the equator - both the lines down to it are the same length (1/4 of the circumference of the sphere). But if you widen the angle at the pole, you can make the line along the equator anywhere from 0 to the full circumference. And then the sin would be up to 4/1 = 4.

The alternative is that parallel lines diverge, called negative curvature or hyperbolic. If you work in hyperbolic space I think sin can be arbitrarily large. But reality is close to Euclidean so I wouldn't worry about it.


I hope that gives you enough information to look stuff up yourself.

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.

Dude, I did the same thing, only in 1st grade. A kid wrote a problem backwards, and the teacher told him he couldn't do that, so I piped up and said it would just be negative.

Does some higher leveled math course for collage math nerds let you input a value into sin, and get 2?

I'm not sure if you're looking to get an answer to arcsin(2) or just this question o.o Anyway, like someone already mentioned, it's possible to find the answer to arcsin(2) by using hyperbolic functions and Euler formula

http://www.wolframalpha.com/input/?i=arcsin+2
Apparently sin(pi/2 +- i*ln(2+sqrt3)) = 2.

I wouldn't be able to tell you why.

I'm sure there's a way to do it. There's always a way to do something, you just gotta prove it.

I taught my brother multiplication when he was in kindergarten lol. That was fun stuff to watch.

http://www.wolframalpha.com/input/?i=arcsin+2
Apparently sin(pi/2 +- i*ln(2+sqrt3)) = 2.

Where the heck did you get that from? o.O

This is the form I'm most familiar with... I'll see what I can dig up on it.


First, we start with what the derivative of arcsin of x is.

Code:

y = arcsin(x)
sin(y) = x
y'cos(y) = 1 <---derivation step
y' = 1/cos(y)
y' = 1/cos(arcsin(x))
y' = 1/sqrt(1-x^2)

General integration formula:
arcsin(a*x) = ʃ(1/sqrt(1-a^2*x^2) * dx)

I'm pretty sure I lost most of you already o.o But we have a workable formula that doesn't involve weird mystery symbols such as sin or ln. To me, this makes the problem of perspective much easier to handle. But if we took it just the way it is, we'll just get arcsin again. So let's do a trick or two...

Code:

ʃ(1/sqrt(1-a^2*x^2) * dx) = ʃ(1/(sqrt(1-a*x)*sqrt(1+a*x)))
Integration by parts

Okay, now I'm not motivated anymore >_>

http://www.wolframalpha.com/input/?i=arcsin+2
Apparently sin(pi/2 +- i*ln(2+sqrt3)) = 2.

I wouldn't be able to tell you why.

Thanks! I wasn't sure of my answer

 Spoiler

Sorry for the extra large font >.> the exponents weren't clear with smaller size .__.

Where the heck did you get that from? o.O

Under "alternate form". I replaced "log" with "ln" (since that's what it is) and sandwiched the expression inside the sin.
sin(arcsin(2)) = 2

Under "alternate form". I replaced "log" with "ln" (since that's what it is) and sandwiched the expression inside the sin.
sin(arcsin(2)) = 2

You don't "sandwich the expression within the sin" at all. It's just:

You don't "sandwich the expression within the sin" at all. It's just:

-blink-
I said that sin(that thing) = 2. Tell me how that's incorrect o_o

-blink-
I said that sin(that thing) = 2. Tell me how that's incorrect o_o

Ahh, just read your last post, not the one further up lol. I see what you did now.