1. Tan,Cos and Sin
Hi
How do I get Tan,Cos or Sin to the power of -1 in Euphoria? I mean that I
give the function a ratio and it gives me the angle. Arctan seems to give
tan to the -1 but how do I get the others?
Thanks :)
--PatRat (Thomas Parslow)
-- ()___()
-- (o o)
-- =\O/=
-- Rat Software
-- http://www3.mistral.co.uk/billparsl/
2. Re: Tan,Cos and Sin
>Hi
>How do I get Tan,Cos or Sin to the power of -1 in Euphoria? I mean that
I
>give the function a ratio and it gives me the angle. Arctan seems to
give
>tan to the -1 but how do I get the others?
>Thanks :)
>--PatRat (Thomas Parslow)
Isn't the inverse of a trig function just the function of the inverse of
the ratio
ex: sin (1/3)
sin^-1 (3/1)
Or is my math too rusty to be talking about it.
Lewis Towsend
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3. Re: Tan,Cos and Sin
Lewis Townsend wrote:
>Isn't the inverse of a trig function just the
>function of the inverse of the ratio
> ex: sin (1/3)
> sin^-1 (3/1)
ummmm no.
sin(1/3) = 0.0058
arcsin(3) = *error*
sin(3) = 0.0523
arcsin(1/3)= 19.471
however, arcsin, and arccos can be calculated with use
of the other functions we have available.
function arcsin(object x)
--returns the arccos expressed in *radians*
--here we know opp and hyp, and we need opp/adj
--we can assume hyp is 1, since we are given opp/hyp
--expressed as a ratio "over 1"
--object opp --we know this already, here for clarity
object adj
--opp=x --for clarity
--adj=sqrt(1-opp*opp) --for clarity
adj=sqrt(1-x*x)
--return arctan(opp/adj)--for clarity
return arctan(x/adj)
end function
function arccos(object x)
--returns the arccos expressed in *radians*
--here we know adj and hyp and we need opp/adj,
--we can assume hyp is 1, since we are given opp/hyp
--expressed as a ratio "over 1"
object opp
--object adj --we know this already, here for clarity
--adj=x --for clarity
--opp=sqrt(1-adj*adj) --for clarity
opp=sqrt(1-x*x)
--return arctan(opp/adj)--for clarity
return arctan(opp/x)
end function
you can test the above functions if you like :)
--Hawke'
4. Re: Tan,Cos and Sin
>>Hi
>>How do I get Tan,Cos or Sin to the power of -1 in Euphoria? I mean
>Isn't the inverse of a trig function just the function of the inverse
of
>the ratio
>ex: sin (1/3)
> sin^-1 (3/1)
Nonono! The inverse of a trig function is actually another function:
tan^-1=arctan
sin^-1=arcsin
etc
When you write arctan(x), what you are really looking for is the angle
which has x as its tan.
The confusion here probably comes from looking at the inverse of a
number versus the inverse of a funcion:
Number: (1/3)^-1=(3/1)
Function: y=f(x), x=f^-1(y)
It's just important to remember that you're looking at trig *functions*,
whose inverses happen to be other trig functions.
Hope that clears up the difference. :)
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5. Re: Tan,Cos and Sin
- Posted by lgregg at BIG12.METROBBS.COM
Oct 07, 1998
-
Last edited Oct 08, 1998
Patrat said:
> How do I get Tan,Cos or Sin to the power of -1 in Euphoria? I mean that I
> give the function a ratio and it gives me the angle. Arctan seems to give
> tan to the -1 but how do I get the others?
> Thanks :)
> --PatRat (Thomas Parslow)
If you look on the official Euphoria Web page:
--Recent User Contributions--
"Math Routines"
--Euphoria Archive--
Mathematics Routines
"Inverse Math Functions"
Library Routines
"Arcsin & Arccos"
Hope they help.
Larry
6. Re: Tan,Cos and Sin
On Wed, 7 Oct 1998, PatRat wrote:
> How do I get Tan,Cos or Sin to the power of -1 in Euphoria? I mean that I
> give the function a ratio and it gives me the angle. Arctan seems to give
> tan to the -1 but how do I get the others?
Like others have said, tan^-1(x) = arctan(x) [not 1/tan(x)].
There's my mathbag.e in PROJECTS.ZIP on my Euphoria Page. I'll put the
link up later today if I remember :)
Lee Woo Seob and I argued quite a bit about mathbag last year. Is Lee
still around? (I think he last posted in March)
--
Carl R White -- Final Year Computer Science at the University of Bradford
E-mail...: cyrek- at -bigfoot.com -- Remove the hyphens before mailing. Ta :)
URL......: http://www.bigfoot.com/~cyrek/
Ykk rnyllaqur rgiokc cea nyemdok ymc giququezka caysgr -- B.Q.Vgesa
7. Re: Tan,Cos and Sin
>How do I get Tan,Cos or Sin to the power of -1 in Euphoria? I mean that I
>give the function a ratio and it gives me the angle. Arctan seems to give
>tan to the -1 but how do I get the others?
Use of terminology in maths can be confusing, as in this case *Sin to the
power of -1*
The same set of symbols mean different ( but in some sense related ) things
depending on context.
For example
If y is a number:-
y^-1 = the reciprocal of y (the inverse of y)=1/y
if y is a function:-
y^-1 is the inverse FUNCTION of y e.g. the inverse function of x^2 is sqrt(x)
and the inverse FUNCTIONof sin is arcsin
if Y is a matrix:-
Y^-1 is the matrix inverse i.e ( Y^-1 )*( Y ) = I ( the unit matrix )
The symbols ^-1 mean different things in each case but they are similar as:-
for a number (y^-1)(y) = 1 ( the number one )
for a function ( y^-1( y(x) ) = x e.g. sqrt( (x*x) ) = x and arcsin( sin(x) )
= x
for a matrix ( Y^-1 )*( Y ) = I ( the unit matrix )
Hope this is helpful.
Also I agree with John Worthington's comments on *Issue of the week*
>no, No, NO! ;') Remember, you have these people like me who really
>enjoy reading these things and learn something. I just don't have much
>to add in here. But PLEASE don't drop threads like this. What seems
>amazing to me is that I am learning, not just Euphoria coding, but about
>programming in general. Anyways, nothing else to say at the moment, so
>keep up the good work. ;')
Neil
