calculus

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shiznatix
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calculus

Post by shiznatix »

ok i need a whole lot of help on this subject. you already know my language barriar situation. heres what i really need to understand

arcsin
sin
cos
ln
log

what we get in a function defined with all the fun fun variables then we have to find the set that x or y or whatever is in. there will be like arcsin(x)^2 and then all of a sudden its multiplied by log and everything goes crazy from there. anyone maybe have any good online tutorials or somthing or maybe some simple explinations on what would cancle eachother out here? definitions would also be lovely as i cant seam to find any.
Charles256
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Post by Charles256 »

you don't really cancel sin out..however going.. arcsin(sin(x)) would leave you with just x....
arccos(cos(x)) also leaves you with x.. taking the log of a ln leaves you with whatever is your variable and vice versa if memory serves me right...good enough?
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Post by timvw »

Could scan some basic courses... but they are in dutch, so i don't think you'll understand those ;)

As always, stfw :)) http://en.wikipedia.org/wiki/Trigonometry
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Ambush Commander
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Post by Ambush Commander »

I don't think that this is Calculus...

Anyway, here's my explanation. Sin(x) is a periodic function, and therefore is not one-to-one (as output values appear multiple times on the graph). For that reason, it doesn't have an "inverse" (f^-1(x)) so to speak. However, we often find it helpful to determine the angle measure from the ratio that is given from Sin(x). We therefore bound the functions between, in Sine's case, 0 <= x < 90. Only values from that area will be returned by your calculator. In a real inverse "function", however, the value of Sin^-1(x) = Arcsin(x) + 360n where n is an arbitrary integer (and can be negative).
what we get in a function defined with all the fun fun variables then we have to find the set that x or y or whatever is in.
I believe you are talking about Domain and Range. In a standard function f(x), the domain is the possible values x may take, and range is the possible values f(x) takes. These are usually defined via set notation.
there will be like arcsin(x)^2 and then all of a sudden its multiplied by log and everything goes crazy from there.
These descriptions are not very helpful. You cannot "multiply" by log persay. Perhaps you could post the original question?
definitions would also be lovely as i cant seam to find any.
A google would work, but essentially:

arcsin - the inverse of sine
sin or sine - the ratio between the opposite side and the hypotenuse of a given angle in a right triangle
cos or cosine - the ratio between the adjacent side and the hypotenuse of a given angle
ln - the natural logarithm of a number. Equivalent to a Log with a base of e.
log or logarithm - This function is the inverse of exponentiation, that is, x^y = z can be rewritten as log_x(z) = y.
e - E is a mathematical constant that is very important. There are multiple definitions of it, which can be viewed here: http://en.wikipedia.org/wiki/E_%28mathe ... onstant%29

Hope that helps. Personally, I'm taking a Pre-Calculus course right now although I know a little Calculus, so my Trigonometry is fresh.
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Post by Charles256 »

yeah.i'm doing proofs to proove calculus is right, right now:-D so sometimes I forget my trig.though it turns out I was right:-D
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shiznatix
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Post by shiznatix »

ok here goes. 2 examples:

Code: Select all

y = arcsin(2x+3)
      ----------------
         ln(x+3/2)

this goes to these laws:
------------------
|  |2x+3| <= 1   ------------i don't understand how this is gotten
|  x+3/2 > 0       -----------i guess you cant take ln to a negative number
|  ln(x+2/3) != 0 -----------makes sence, you can't divide by 0!
------------------

then it breaks off into simplifing each equation. the one one i don't understand is this

c)  ln(x+3/2) != 0
    x+3/2 != 2 -----how did this line happen?
    x != .5
that is number one. that kinda makes sence but things just seam to appear every now and then

number 2:

Code: Select all

3^(y-sinx) = 10^x
log3(y-sinx) = log10^x -----why log this stuff?
(y-sinx)log3 = x log10 -------i kinda understad, i think...
(y-sinx)log3 = x ----------how is the log of 10 = 1?
.....the rest makes sence
that is all i will bother you with now. thanks if you can explain any of that.
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Post by Charles256 »

|2x+3| <= 1

the hell?when is that EVER true?
x=0, 3 !<= 1, so umm..yeah..there's a case where it's not true (i'd bet my ass it's NEVER true since it's in absolute value symbols) so that whole statement is boulder dash..and if it's not please define where it is true for me:-D
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Post by Ambush Commander »

I'm working on it, but in reply to Charles256

Code: Select all

x = -3/2
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Post by Ambush Commander »

Code: Select all

|2x+3| <= 1 from arcsin(2x+3)
Again, there's a bounded domain. You cannot put any old x inside an arcsine and expect an answer: arcsin only accepts values between -1 and 1. |2x+3| <= 1 is a fancy way of saying that.

Code: Select all

ln(x+3/2) != 0
x+3/2 != 2
I assume they did a bit of trickery because we need to prove that x != 1/2. This cannot be explictly proved from the above statement, instead...

Code: Select all

|2x+3| <= 1
2x+3 <= 1 AND 2x+3 >= -1
x+3/2 <= 1/2 AND x+3/2 >= -1/2
THEREFORE x + 3/2 != 2
Not exactly sure why you needed x != 1/2 though...

Code: Select all

3^(y-sinx) = 10^x
log(3^(y-sinx)) = log(10^x)  --- Your presentation of the equation was ambiguous ;)
(y-sinx)log3 = x log10 ---- We logged both sides in order to do this sort of trickery
(y-sinx)log3 = x --- try it in a calc. log is short hand for log10, and logx(x) = 1
Hope that helps.
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Post by Charles256 »

note to self: don't do basic math when fighting a hang over...
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shiznatix
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Post by shiznatix »

OK! excellent. last question out of this set of stuff:

Code: Select all

|2x+3| <= 1
2x+3 <= 1 AND 2x+3 >= -1
x+3/2 <= 1/2 AND x+3/2 >= -1/2
THEREFORE x + 3/2 != 2 ------how do you get 2? am i missing somthing completly obvious.
the rest of that I understand. many thanks! hopefully i will pass my test tomarow
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Post by Ambush Commander »

Well... two is greater than 1/2 and the x + 3/2 has to be less than 1/2 so it cannot possibly equal two.

The real question is why two?. Why not three? Or four?
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