# Two Cans & String

ForumTechnical Corner ► Math Problem Thread
If you have math problems, post here.

Not really a problem but just a question.

Explain how Sine-1 turns sine into an angle, usually theta :P

Arcsine undoes Sine. The information you gather from a triangle is the Sine of ABC, which is not useful in finding the angle measurement. We can undo Sine though with Arcsine, just like how the sqrt(x2) == x.

At least, I think that's how it is explained.

This might be a bit vague, but here goes.

Given: (x+3)^2

Find: f(x+h)

Any help?

Arcsine undoes Sine. The information you gather from a triangle is the Sine of ABC, which is not useful in finding the angle measurement. We can undo Sine though with Arcsine, just like how the sqrt(x2) == x.

At least, I think that's how it is explained.

... but how does putting sine under a sign that means "basically" to give the reciprocal... how does that worK?

This might be a bit vague, but here goes.

Given: (x+3)^2

Find: f(x+h)

Any help?
Are you not given the original function f? I'm a little lost as to what is being asked.

I'm only asking why you get the angle that creates the ratio of Sine when you press Sin-1 Yes, I understand what ArcSine is, but how does getting a reciprocal reproduce the angle?

Ah, it's not a reciprocal. The symbol is a bit misleading. The -1 simply means that it's the inverse function, not that it's the multiplicative inverse (reciprocal).

Edit: In other words, sin-1 is just a function designed to return the angle that yields whatever sine value is given it.

The -1 doesn't actually mean the reciprocal - it's notational shorthand for arcsin.

In the same way that x-1(x(a)) = a, sin-1(sin(a)) = a.

Also, to the function question:
If you mean that f(x) = (x + 3)2, then f(x+h) = ((x+h)+3)2. Everywhere you see x in the original function, replace it with (x+h).

Ah, it's not a reciprocal. The symbol is a bit misleading. The -1 simply means that it's the inverse function, not that it's the multiplicative inverse (reciprocal).

so what's an inverse function?

It is a function that "undoes" a corresponding function. The inverse of the function "f(x) = x + 1" for example would be "f-1(x) = x - 1".

This might be a bit vague, but here goes.

Given: (x+3)^2

Find: f(x+h)

Any help?
Are you not given the original function f? I'm a little lost as to what is being asked.

So am I. But its on my homework and I haven't the slightest clue on what to do. I don't even know what it is asking. Oh well...

This might be a bit vague, but here goes.

Given: (x+3)^2

Find: f(x+h)

Any help?

I dunno. If f(x)=(x+3)2, then f(x+h) would be:
f(x+h)=[(x+h)+3]2
f(x+h)=(x+h+3)2
f(x+h)=x2+h2+9+2hx+6x+6h
f(x+h)=x2+(2h+6)x+h2+6h+9

Thank you Beary! You are a cool cat.

If this is just a derivative, when f(x)=(x+3)^2, f'(x) = 2(x+3). Easy :)

Hoooly shit, I'm so fucked if there is no one here to help me, like now!

I have homework due tomorrow, 3 questions only, but I don't know shit about them!
And here it's 10:35 pm!

If this is just a derivative, when f(x)=(x+3)^2, f'(x) = 2(x+3). Easy :)

Err, wouldn't it be (x+3)*(x+3), which would make the answer x^2+6x+9? The complications arise when h is introduced. But no matter. I've already turned it in.

Err, wouldn't it be (x+3)*(x+3), which would make the answer x^2+6x+9? The complications arise when h is introduced. But no matter. I've already turned it in.

No, it wouldn't. The Power Rule easily proves when f(x) = (x+3)^2, f'(x) = 2(x+3).

As for when h is used, as above, f(x + h) is usually used as part of the formula "lim(h-->0) ( ( f(x+h) - f(x) ) / h )", which, if f(x) = (x+3)^2, will equal 2(x+3). Ok, thank you very much. I'm going in for tutorials tomorrow. I obviously don't understand it at all.

ywkbme said:
I have homework due tomorrow, 3 questions only, but I don't know shit about them!
And here it's 10:35 pm!

Let us help. O_o

I'm fine, a friend helped me! :D

My math teacher says that if you've got a geometry problem, and you can't make sense of it, draw random lines that pass through at least one point (preferably 2). You'll eventually get a line that'll make you click.
Not really a problem but just a question.

Explain how Sine-1 turns sine into an angle, usually theta :P

Well, if sin(theta) gives the sine of an angle, then Sin-1(theta) should do the inverse... right?

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