Re: solution of equation

• To: mathgroup at smc.vnet.net
• Subject: [mg116390] Re: solution of equation
• From: Peter Breitfeld <phbrf at t-online.de>
• Date: Sun, 13 Feb 2011 03:05:40 -0500 (EST)
• References: <ij5mvj\$jo5\$1@smc.vnet.net>

```Piotr Munik wrote:

> Dear Math Group,
>
>
>
> I want to solve equation like this:
>
> L := 100; h := 1;
>
> n Tan[n L] == h
>
>
>
> I need roots of this equation in a list form
>
>
>
> but I have a problem.
>
>
>
> I try findfoot
>
> FindRoot[n Tan[n L] == h, {n, 0.01}]
>
> but it's not good
>
>
>
>
>
> Piotr
>
>

Try Reduce:

sols={ToRules@Reduce[{n Tan[n L] == h, 0. <= n <= 1}, n]}

Out={{n -> 0.0155525}, {n -> 0.0466577}, {n -> 0.0777637},
{n -> 0.108871},  {n -> 0.139981},  {n -> 0.171093}, {n -> 0.202208},
{n -> 0.233327},  {n -> 0.26445},   {n -> 0.295577}, {n -> 0.326709},
{n -> 0.357847},  {n -> 0.388989},  {n -> 0.420138}, {n -> 0.451292},
{n -> 0.482452},  {n -> 0.513618},  {n -> 0.54479},  {n -> 0.575969},
{n -> 0.607154},  {n -> 0.638345},  {n -> 0.669543}, {n -> 0.700746},
{n -> 0.731956},  {n -> 0.763171},  {n -> 0.794393}, {n -> 0.82562},
{n -> 0.856853},  {n -> 0.888092},  {n -> 0.919336}, {n -> 0.950585},
{n -> 0.981839}}

I wrote "0." instead of "0" in the inequality to get Reals in the