calculus
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- shiznatix
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calculus
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.
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.
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Charles256
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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
As always, stfw
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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).
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.
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).
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.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.
These descriptions are not very helpful. You cannot "multiply" by log persay. Perhaps you could post the original question?there will be like arcsin(x)^2 and then all of a sudden its multiplied by log and everything goes crazy from there.
A google would work, but essentially:definitions would also be lovely as i cant seam to find any.
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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Charles256
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- shiznatix
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ok here goes. 2 examples:
that is number one. that kinda makes sence but things just seam to appear every now and then
number 2:
that is all i will bother you with now. thanks if you can explain any of that.
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 != .5number 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-
Charles256
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I'm working on it, but in reply to Charles256
Code: Select all
x = -3/2- Ambush Commander
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Code: Select all
|2x+3| <= 1 from arcsin(2x+3)Code: Select all
ln(x+3/2) != 0
x+3/2 != 2Code: 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 != 2Code: 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-
Charles256
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- shiznatix
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OK! excellent. last question out of this set of stuff:
the rest of that I understand. many thanks! hopefully i will pass my test tomarow
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.- Ambush Commander
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