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Best answer by LucMeekes

Cannot be solved.

The tan function is periodic. A one-to-one relationship exists only if you limit the argument of the tan function between -pi/2 and pi/2.

In your 3rd and 4th lines that is not the case.

You'll find the very same problem if you change 'tan' to 'sin' in your expressions.

For 'cos' it is slightly different.

 

Success!
Luc

2 replies

L
LucMeekes23-Emerald IVAnswer
23-Emerald IV
January 14, 2021

Cannot be solved.

The tan function is periodic. A one-to-one relationship exists only if you limit the argument of the tan function between -pi/2 and pi/2.

In your 3rd and 4th lines that is not the case.

You'll find the very same problem if you change 'tan' to 'sin' in your expressions.

For 'cos' it is slightly different.

 

Success!
Luc

    V
    24-Ruby IV
    ValeryOchkov24-Ruby IVAuthor
    24-Ruby IV
    January 14, 2021

    I see

    W
    Werner_E25-Diamond I
    25-Diamond I
    January 14, 2021

    If you use tan(..) then a lot of information about the angle is lost and can't be brought back.

    The atan function is not the true inverse of tan but is limited per definitionem  to the range [-pi; pi] to make it a unique function.

    But if you don't use numeric inline evaluation when calculating t, symbolic solver "remembers" where it came from - at least as long as ar rational and not given as float value.

    Werner_E_0-1610626664697.png

    In real Mathcad you can create your own atan-function to do the job:

    Werner_E_1-1610626714092.png

    But it will only work if you evaluate it symbolically 😉

     

     

     

     

      V
      24-Ruby IV
      ValeryOchkov24-Ruby IVAuthor
      24-Ruby IV
      January 14, 2021

      Thanks!

       But если нельзя, но очень хочется, то можно. How it is in English?

      I will show one solution fpr one my problema with ovals!

      Now I am creating the animation!

       

      W
      Werner_E25-Diamond I
      25-Diamond I
      January 14, 2021
      @ValeryOchkov wrote:

      Thanks!

       But если нельзя, но очень хочется, то можно. How it is in English?

      Not sure, maybe something like "What does not fit is made to fit" or "You can achieve anything if you really want to" ?

      In fact, my suggestions weren't entirely serious. There is hardly a way to get Mathcad to read your mind to guess what angle you actually are looking for.

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