Posted by Brad Paul on October 19, 2002 at 11:37:39:
In Reply to: explanation please. thanks, but... posted by Barry on October 19, 2002 at 11:03:44:
: Thanks Mr P; BUT
: : How you wonder? Use a series representation of sin(t) and
: : cos(t). I will not do it here because it is easy to do but hard to
: : format. Just write out the first few terms of the series for cos(t)
: : then use everyones favored derivative equation and you will start to
: : see that you are generating the terms for the -sin(t) series.
: it's this "sin/cos" stuff I'm not familiar with (as you say).
: what is "a cos/sin series" ?
Every function can be written as a series.
The series representation for cos(t) about t=0 is:
The series representation for sin(t) about t=0 is:
where n!=n*(n-1)*(n-2)*...*2*1 example:
Now write out on paper the terms for the cos(t) series. (You can even
follow the pattern and write out more terms that I gave you)
Then take the derivative of each term and you will find that you have
the series representation of -sin(t).
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