is cotx equal to 1/tanx
Lax
hdbanannah
> is cotx equal to 1/tanx?
Yes.
Christopher Henrich
<a2e360d1-40a7-4e34...@o15g2000yqm.googlegroups.com>,
hdbanannah <hdban...@aol.com> wrote:
> 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
Patrick Coilland
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.
David W. Cantrell
> is cotx equal to 1/tanx?
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
David W. Cantrell
> hdbanannah a �crit :
> > On Aug 21, 2:20 pm, Lax <lax.cla...@gmail.com> wrote:
> >> is cotx equal to 1/tanx?
> >
> > Yes.
>
> being very rigorous, no :
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
A N Niel
<8195940e-e16e-4e97...@c29g2000yqd.googlegroups.com>,
Lax <lax.c...@gmail.com> wrote:
> is cotx equal to 1/tanx?
As meromorphic functions, yes.
Eudickhead
"hdbanannah" <hdban...@aol.com> wrote in message
news:a2e360d1-40a7-4e34...@o15g2000yqm.googlegroups.com...
>No, cotx = Cosx/sinx
Go blither somewhere else, AOL asshat.
The Sortov Institute
> is cotx equal to 1/tanx?
Yes if you type it right. (That's the point of Dr. Banannah's reply btw.)
William Elliot
M.M.M.
On Aug 22, 3:48 am, William Elliot <ma...@rdrop.remove.com> wrote:
> What is the Sortov Institute?
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
JEMebius
> is cotx equal to 1/tanx?
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).
David W. Cantrell
> Lax wrote:
> > is cotx equal to 1/tanx?
>
> 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.
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
The Sortov Institute
"William Elliot" <ma...@rdrop.remove.com> wrote in message
news:2009082203...@agora.rdrop.com...
> What is the Sortov Institute?
An informal society of low-profile superstars.
Scribe
total results: 3,854 for cot(X) = 1/tan(X) whenever tan(X) <> 0 and cot(X) <> 0.
Graphs of the Trigonometric 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. ...
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) ...
Full text of "A treatise on the differential calculus with numerous ...
When x = 0, y = 0, and when x has any positive value, y is a ... of tan -1 ic and cot" 1 a;. Let y = tan -1 ic, therefore x = tan y, therefore -r- = , Art. ...
\... tan y = 1/x, y = tan1 (1/x); if x < 0 then π/2 < y < π and x = cot y = cot(y π) ... whenever k > 1/0.368 2.717. y 2 -2 x (c) x 1.155 13. ln y = ln 5000 ...
Solve on the interval [0,2pi) : cot x (tan x + 1)=0?
Whenever cotx=0 and when tanx=-1. This corresponds to 90, 135, 270, 315.
part II
.. x > 0, and thus the derivative for x > 0 is 1/x. ... cot x = cosec. 2. x whenever cot x is defined. 8. Proof. d. dx cot x = d. dx. 1. tan x. d. dx (tan x) tan. 2 ...
CH1
.. (x + y), cot x, and cot y. sin(4x), sin x, and cos x. cos x and cos x/2. tan ... how long it takes for the maximum at x = 0 at t = 0 to reach x = 1 and x = -1. ...
www.usna.edu/Users/math/rmm/PROGRAMS/ch1.html
1. Derivatives The derivative f
h0. f (x + h) f(x) h. whenever this limit exists. ... (6) cot x = a/o = cos x/ sin x = 1/ tan x ... but all functions except tan and cot have a negative sloped ...
.. csc x _ , 0° x 90° 4 13 _ , 270° θ 360° b) sec θ 12 24 _ , 90° x 180° c) cot x 7 ... identity tan x _ is true for x 40°, cos x x 110°, x 232°, and x 355°. PROBLEM ...
Scribe
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
William Elliot
> "William Elliot" <ma...@rdrop.remove.com> wrote in message
>> What is the Sortov Institute?
>
> An informal society of low-profile superstars.
>
Who are the informal members?
Phil Carmody
> What is the Sortov Institute?
Sort-of a joke, I think.
Phil
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