# sin(x)^2+cos(x)^2->? as x->Infinity

erikkonstas shared this problem 2 years ago
New

This is the command I've tried, after entering it in the GeoGebra app (Android, up to date):

Limit(sin^(2)(x)+cos^(2)(x),∞)

It shows "?", while it should be 1.

1

Which GeoGebra app?

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CAS, forgot to mention.

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classic answer undefined also limit(simplify(),inf) says 1

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What?

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cos(x), sin(x), cos²(x), sin²(x), cos²(x) + sin²(x)

all those function don't have a limit when x--->∞

It is not a GeoGebra error : GeoGebra give the good answer : undefined (good answer) : 1 is wrong answer

if you simplify : Simplify(cos²(x) + sin²(x)) = 1

So limit(Simplify(cos²(x) + sin²(x))) = limit (1) = 1..!

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Hm, maybe it should work without an explicit simplification command?

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Hm, if at a mathematical exam you say :

limit(cos²(x) + sin²(x))=1 when x-->∞

i say "why" and i don't give you 20/20

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And I say "by the famous identity...", just one more step GeoGebra should take.

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GeoGebra is a bad boy : he doesn't know famous identity phew

Seriously : i am teacher and i am very happy when a machine force students to... think..! (and your example is a very good example... very instructive). We must give them critical mind...

The machine should do everything perfectly ? so we don't have to think ? it is a point of view...

Hope for you developers will do this...

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So you'd accept a machine to be plain wrong instead of trying to fix it... nice approach man, nice approach, you'll definitely get a good sheeple out of it. Good luck...

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i gave you (in my first post) my point of view (and i didn't insult you...)

Good luck to you too man