Re: inequations & trig. eq

To: CALC-TI@LISTS.PPP.TI.COM
Subject: Re: inequations & trig. eq
From: "Groppa S." <groppa@ch.moldpac.md>
Date: Wed, 28 Jan 1998 16:03:37 +0200
References: <v01540b02b0f48111bd6c@[206.40.98.68]>
Reply-To: groppa@ch.moldpac.md

Hi, Thanks a lot for the answer

Yes, but how to solve x/(x-1) undefined ?

and if the inequation is  a little bit difficulter for ex
(sinx-2)/(4sin^2 x -1)>2

Many thanks in advance
Sincerely
Ser

>
> Yes the TI-85/86 can be used for solving Trig. equations and
> solving inequalites.
>
> Use graphing and use SOLVER to find solutions to equations, these
> same procedures that work for equations in general will work for
> the specific trig. equations.
>
> Graphing, SOLVER, and POLY, can also aid in solving inequalities.
>
> Theorem:  Let f(x) be any expression with the single variable x.
>           Then for any real number a one of the following must be true:
>
>           1.  f(a)=0
>
>           2.  f(a)>0
>
>           3.  f(a)<0
>
>           4.  f(a) is undefined.
>
> To solve f(x)>0 or f(x)<0  first solve f(x)=0 and f(x) undefined.
>
> Example:Solve  x/(x-1) > 0
>
> Solution:  Fisrt solve x/(x-1)=0 and x/(x-1) undefined.
>
>                      x=0               x = 1
>
> Plot these 'critical' points.
>
> <-----------------0-----------1---------------->
>
> Note the real number line is cut into three regions. Use a test
> point for each region. A test point should be completely inside
> the region.  -10  will work for the left region,  .5 for the middle
> region , and 20 for the right region. (Any point in a region will do.)
> Check each of these test points. If the test point checks so
> does all the other points in same region it comes from. If it does not
> then none of the other of that region will check either.
>
> <-----------------0-----------1---------------->
>         -10           .5             20
>
>  -10/(-10-1) > 0   .5/(.5-1) > 0     20/(20-1) > 0
>
>       Yes                 No            Yes
>
> So the solution to
>
>                 x/(x-1) > 0
>
> is
>                 x<0  or   x>1
>
> To find these 'critical' values and to check the test points
> calculators can be of great assistance. The TI-85/86 is truely
> great at this.
>
> The graphing features of TI-85/86 can also be used in solving
> inequalites.
>
> If you graph   y=x/(x-1)
>
> 1. The x-intercepts correspond to where  x/(x-1)= 0.
>
> 2. The region(s) where the graph is above the x-axis corresponds to the
>    subset where x/(x-1)>0.
>
> 3.The region(s) where the graph is below the x-axis corresponds to the
>   subset where x/(x-1)<0.
>
> 4.The region(s) where there is no graph corresponds to where x/(x-1)
>   is undefined.

References:

From: