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From: Michael Stemper on 29 Jul 2010 09:12
In article <8bd5sqFrciU1(a)mid.individual.net>, =?ISO-8859-1?Q?Jos=E9_Carlos_Santos?= <jcsantos(a)fc.up.pt> writes:
>On 29-07-2010 11:12, William Elliot wrote:

>> What are the solutions to the equations
>>
>> sin^-1 x = 1/sin x,
>
>Obviously, it has one and only one solution, namely 0.

Huh? sin(0) = 0, so what's i/sin(0) ?

--
Michael F. Stemper
#include <Standard_Disclaimer>
Indians scattered on dawn's highway bleeding;
Ghosts crowd the young child's fragile eggshell mind.
From: Ray Vickson on 29 Jul 2010 12:25
On Jul 29, 4:14 am, José Carlos Santos <jcsan...(a)fc.up.pt> wrote:
> On 29-07-2010 11:12, William Elliot wrote:
>
> > What are the solutions to the equations
>
> > sin^-1 x = 1/sin x,
>
> Obviously, it has one and only one solution, namely 0.

A reveals a solution near 0.9. Maple gives:
fsolve(arcsin(x)=1/sin(x),x=.8.. .95);
0.9440390666 <---- numerical solution

Certainly, x = 0 is not a solution.

>
> > cos^-1 x = 1/cos x?
>
> It has one and only one solution, around 0.739085. I doubt that it is
> "nice" number.

Again, a plot reveals a solution near 0.4 and Maple gives
fsolve(arccos(x)=1/cos(x),x=.4 .. .8);
0.4460476800 <--- numerical solution

R.G. Vickson

>
> Best regards,
>
> Jose Carlos Santos

From: Passerby on 29 Jul 2010 14:19
On Thu, 29 Jul 2010 03:12:10 -0700, William Elliot
<marsh(a)rdrop.remove.com> wrote:

>What are the solutions to the equations
>
> sin^-1 x = 1/sin x,

x ~~ +-0.9440390666116078...

>
> cos^-1 x = 1/cos x?

x ~~ 0.446047679999125754...

From: gudi on 29 Jul 2010 15:22
On Jul 29, 3:12 pm, William Elliot <ma...(a)rdrop.remove.com> wrote:
> What are the solutions to the equations
>
>         sin^-1 x = 1/sin x,
>
>         cos^-1 x = 1/cos x?

The only real roots are approx 0.944039 and 0.446048 respectively, and
the periodic complex roots ( period = pi ) can be iterated from
complex Newton-Raphson.

Narasimham
From: gudi on 29 Jul 2010 15:29
On Jul 29, 3:12 pm, William Elliot <ma...(a)rdrop.remove.com> wrote:
> What are the solutions to the equations
>
>         sin^-1 x = 1/sin x,
>
>         cos^-1 x = 1/cos x?

The only real roots are approx (+/-)0.944039 and 0.446048
respectively, and the periodic complex roots ( period = pi ) can be
iterated from complex Newton-Raphson method.

Narasimham
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