5-Regular Member

Question

Expansion formula for cos(n*x) yields unexpected results

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The following Mathcad code attempts to use a formula from Wikipedia to expand cos(n*z), but appears to get the wrong result. Comments?

Mathcad code implementing expansion formula

V

VladimirN

24-Ruby IV

It's better to attach your file in the archive here.

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AD_2895922

Author

5-Regular Member

Great! I looked for somewhere to upload my file, but couldn’t find it. How do I do it?

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DJNewman

19-Tanzanite

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PTC Marketer for Creo and Mathcad. I run their YouTube channels, some Creo campaigns, and all Mathcad campaigns and communications.

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AD_2895922

Author

5-Regular Member

Image file of embedded picture in the original post

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LucMeekes

23-Emerald V

That is still a picture.

Better is to upload the prime worksheet file ( .xmcd).

But you will have to .zip it first and upload that .zip file.

Also you should indicate which version of Prime you are using.

Success!

Luc

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Werner_E

25-Diamond I

I can’t test it in Prime as I have no access to a full version of Prime, but I agree that Prime’s result of the symbolic evaluation which you highlighted in yellow is wrong. It should be cos(2z), equivalent to 2 cos²(z)-1 as you wrote.

You may consider contacting official PTC support and report this bug in the symbolic engine.

BTW, interestingly its even worse in legacy Mathcad 15 (with muPad as its symbolic engine):

The error messages displayed are confusing and I can't make sense of them.

My first guess was that it may have to do with a faulty implementation of the ‘combin’ function, but this seems not to be the case:

Nonetheless MC15’s symbolics returns wrong results. Calculation of the following two expressions should be the same as “i” only has the value 0. Nonetheless only hard coding the zero as limit of the second sum gives the correct result.

Mathcad 15 is not supported anymore and so bugs in this legacy version will not be fixed. But since Prime is based on Mathcad, it's possible that a bug from the older version was carried over to Prime.

I attach the file in MC11 format so maybe @LucMeekes would like to give it a try with his Mathcad 11 (which uses Maple for symbolic evaluations).

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Symbolic_Bug_MC11.zip