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I have the following vector function:

$ r(t)=(t-\sinh t\cosh t)\,\partial_x+2\cosh t\,\partial_y. $

I computed its velocity to be as such:

$ r'(t)=-2\sinh^2t\,\partial_x+2\sinh t\,\partial_y. $

Therefore, its speed is as follows:

$ v(t)=2\sinh t\cosh t. $

However, when I computed this using Maple, the program (after simplifying) gave me this:

$ v(t)=2\sqrt{\sinh^2t\cosh^2t}. $

Why did it not get rid of the radical?

Edit: Here is the Maple code:

                                             enter image description here

  • 0
    Does Maple assume that $t$ is complex by default? It may avoid reducing the square root in case $t$ has an imaginary part.2012-10-03

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Probably because the speed is $ 2 \; \cosh t \; \; | \sinh t | $