Avec calcul formel , la résolution de l'équation sqrt(sin(x)) + cos(x) = 1 est incorrecte

barakatomar1960 shared this question 4 months ago
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Comments (9)

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Please post your file and the result you are expecting, as well your OS and GeoGebra version.

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I think it's a bug (GGB-Algebra and/or GGB-CAS ).

Windows 10, GGB 5.0.553

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I think that this equation needs to be solved in CAS.

GeoGebra problem is that it gives the extra solution in x=pi+2k pi, where the square root is not defined in R.

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sqrt(sin(pi+2k pi))--->0

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Oh, sorry!

I’ve misread the parenthesis, and thought that the square root contained both sine and cosine functions!

Damn. I need holidays :(

Have a nice Sunday, mathmagic,

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directly from the help notes of the command

Sometimes you need to do some manipulation to allow the automatic solver to work, for example

sin(x)=(1-cos(x))^2

https://wiki.geogebra.org/e...

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That’s clever!

And it works.

I’m wondering what went wrong with the original equation. Maybe something related to the period of the solutions?

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Anyway, solving the equation “old style”, that is paper and pencil, the extra solution is pi +2k pi, and the other two are correct.

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I think the problem is in continuity

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