trig solutions

[diane....@gmail.com]

Solving the equation (cos(x))^2 + cos(x)tan(x) - sin(x) = 0, the
Nspire and CAS returns a solution of 1.57 - both graphically and with
tracing the graph. Solving the equation does the same. If I go back
to the TI-84 and do the same tracing on the graph or a table of
values, pi/2 returns an error message with the table and a blank with
tracing.

How can I get the Nspire and CAS to give the correct solution? Is
this typical with other functions also?

Any thoughts?
diane

[Nelson Sousa]

note that the TI-Nspire CAS also outputs a warning saying that the domain of the solution may be larger that the domain of the input, which is the case. 

What happens is that the TI-Nspire simplifies cos(x)*tan(x) =sin(x) before solving the equation. Therefore, you get cos(x)+sin(x)-sin(x)=0 <=> x=Pi/2 + 2*n1*Pi (n1 is an arbitrary integer), which is the solution displayed. The problem is that this value is outside the domain of the original equation, being that tan(Pi/2) is undefined, but this singularity is removed when we multiply by cos(x).

This happens a lot when solving equations that have singularities. The simplification takes place before the equation is solved and a warning message indicates that we should manually check the solution.  Computing

cos(x)^2+cos(x)tan(x)-sin(x) | x=Pi/2 returns undef and

cos(x)^2+cos(x)tan(x)-sin(x)=0 | x=Pi/2 returns false,

which is expectable.

Beware of the warning messages displayed by the TI-Nspire CAS on the bottom of the screen. They usually mean that we must look at the results with caution (e.g.: "More solutions may exist", "Questionable accuracy", etc.)

Nelson

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[John Hanna]

Re:  Beware of the warning messages displayed by the TI-Nspire CAS on the bottom of the screen.

If you are using the 2.0 handheld (TouchPad), you can click on this warning with the mouse cursor and see the entire warning.

If you are using the original ClickPad (NavPad) handheld (or the new one), highlight the expression that generated the warning and press ctrl-menu (that’s the equivalent of a ‘right-click’) and select ‘see warning info.’

 

What struck me about the original problem ((cos(x))^2 + cos(x)tan(x) - sin(x) = 0) was that it contains a tan(x) function which is undefined at x=pi/2, so why would anyone expect pi/2 to be a solution in the first place?

 

Nelson’s response is thorough and precise, as usual J.

John Hanna

jeh...@optonline.net

www.johnhanna.us

T³ - Teachers Teaching with Technology

"Reality is an approximation."

 

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[Diane Broberg]

I guess my frustration is that the 84 addressed the issues of a singularity and now the Nspire does not.  Students are often confused when the calculator gives a solution that does not exist.  I agree that the equation is undefined at x = pi/2 and thus my struggle that the calculator returns that as a solution.  I am more curious how the Nspire solves the equat

[Michael Ball]

Wow! I didn't realize you could do this! THANKS!! It's quite
useful. :)

On Mar 19, 12:42 pm, John Hanna <johneha...@gmail.com> wrote:
> Re:  Beware of the warning messages displayed by the TI-Nspire CAS on the
> bottom of the screen.
>
> If you are using the 2.0 handheld (TouchPad), you can click on this warning
> with the mouse cursor and see the entire warning.
>
> If you are using the original ClickPad (NavPad) handheld (or the new one),
> highlight the expression that generated the warning and press ctrl-menu

> (that's the equivalent of a 'right-click') and select 'see warning info.'
>