Yes.
> On Aug 21, 2:20�pm, Lax <lax.cla...@gmail.com> wrote:
> > is cotx equal to 1/tanx?
>
> No, cotx = Cosx/sinx
Well, tan(x) = sin(x)/cos(x), so ... yes, cot(x) = 1/tan(x).
Some good reference web sites: <http://eom.springer.de/>,
<http://mathworld.wolfram.com/>
--
Christopher J. Henrich
chen...@monmouth.com
http://www.mathinteract.com
"A bad analogy is like a leaky screwdriver." -- Boon
being very rigorous, no :
tanx is not defined for x=pi/2+kpi, so is 1/tanx, while cotx is defined
for x=pi/2+kpi, so these two functions dont have the same domain.
cot(x) = 1/tan(x) and tan(x) = 1/cot(x) as long as x is not an integer
multiple of pi/2, and perhaps you knew that already. So maybe you asked the
question because you wonder if there is a way in which we can legitimately
say that
cot(x) = 1/tan(x) and tan(x) = 1/cot(x)
_always_ hold. Well, there is such a way. If we allow the codomains of the
tangent and cotangent functions to be R* = R U {oo}, the one-point
extension of the reals, rather than restricting their codomains to just the
reals, then cot(x) = 1/tan(x) and tan(x) = 1/cot(x) always hold. See
<http://mathworld.wolfram.com/ProjectivelyExtendedRealNumbers.html> for
information about R*.
David
Right, assuming that we restrict codomains to the reals. But, as I just
mentioned in this thread, if we allow the codomains to be the one-point
extension of the reals, then
being very rigorous, yes
David
> is cotx equal to 1/tanx?
As meromorphic functions, yes.
>No, cotx = Cosx/sinx
Go blither somewhere else, AOL asshat.
Yes if you type it right. (That's the point of Dr. Banannah's reply btw.)
Trig: Verify Identity: Cot(x)/[1-Tan(x)] + Tan(x)/[1-Cot(x)] = 1+ Tan
(x
LHS = cot(x) / (1-tan(x)) + tan(x) / (1 - cot(x)) = (1/tan(x)) / (1 -
tan(x)
Prove the Identity: (cot x/1-tan x)+(tan x/1-cot x) =1+ tan x+ cot x?
cotx tanx - + -1-tan x 1- (1/tan x ) = cotx (tanx)^2 - - -1-tan x 1-
(tan x ) = cotx - (tanx)^2... 1-tan x 1- (1/tan x ) = cotx (tanx)^2 -
- -1-tan x 1
--Musatov
Yes: below a proof beginning with the AFAIK original definition of the cotangent function.
Like the cosine of X is defined as the sine of the complement (*) of X, the cotangent of X
is defined as the tangent of the complement of X.
So we have
cot(X) = tan(90-X) = sin(90-X) / cos(90-X) = cos(X) / sin (90-(90-X)) =
= cos(X) / sin(X) = 1 / tan(X)
wherever tan(X) <> 0.
Johan E. Mebius
(*)
----------------------------------------------------------------------
Complement of angle X is its completion to a right angle (90 degrees);
supplement is its completion to a straight angle (180 degrees).
But surely that isn't your only restriction. Apparently, you're intending
to use just the real numbers as the codomain of the functions, in which
case one could properly say
cot(X) = 1/tan(X) whenever tan(X) <> 0 and cot(X) <> 0.
[But, as I'd mentioned earlier in this thread, if we use the one-point
extension of the reals for the codomain, then cot(X) = 1/tan(X) and
tan(X) = 1/cot(X) hold without restriction.]
David
An informal society of low-profile superstars.
igonometric Functions
cot x = 1 / tan x. Whenever tan x = 1, cot x = 1. Whenever tan x = -1, cot x = -1. Whenever tan x = 0, cotangent is undefined and its graph has a vertical asymptote. ...
jwbales.home.mindspring.com/precal/part4/part4.3.html
Elementary mathematical functions in MATLAB
whenever n is a multiple of 3. Thus, an integer number n is ... The reason for this result is that, as x 0, cot(x) ± , since tan(0) = 0, and cot(x) = 1/tan(x) ...
satov
>> What is the Sortov Institute?
>
> An informal society of low-profile superstars.
>
Who are the informal members?
Sort-of a joke, I think.
Phil
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