# Re: explanation please. thanks, but...

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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:
cos(t)=1-t2/(2!)+t4/(4!)-t6/(6!)+...

The series representation for sin(t) about t=0 is:
sin(t)=t-t3/(3!)+t5/(5!)-t7/(7!)+...

where n!=n*(n-1)*(n-2)*...*2*1 example:
4!=4*3*2*1=24

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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