Best wishes and Good luck in your first year.

Crib notes or Cheat sheets.
"Trigonometry"
e^(iwt) = cos(wt) + isin(wt)
i^2 = -1 and +i = squareroot(-1).
-> 2(i)sin(wt) = [e^(iwt) - e^(-iwt)].
-> 2cos(wt) = [e^(iwt) + e^(-iwt)].
-> 2sinh(wt) = [e^(-i(iwt)) - e^(i(iwt))] = [e^(wt) - e^(-wt)]= 2sin(-iwt)) = -2sin(iwt).
-> 2cosh(wt) = (e^(-i(iwt)) + e^(i(iwt))) = (e^(wt) + e^(-wt)) = 2cos(iwt).
Further identities and such can be easier if
e^(iwt) = cos(wt) + isin(wt) is used instead of your noodle.
aside (that I found interesting): e^(irwt) = cos(rwt) + isin(rwt) = (cos(wt) + isin(wt))^r.
"polar notation".
"(angle)" being that "
Reply to
Simon Roberts
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e^(irwt) = cos(rwt) + isin(rwt) = (cos(wt) + isin(wt))^r. > > > > > > "polar notation". > > > > "(angle)" being that "
Reply to
Simon Roberts
to be honest my refresher but if it help i'm happy.
"Trigonometry" e^(iwt) = cos(wt) + isin(wt) i^2 = -1 and i = squareroot(-1). 2(i)sin(wt) = [e^(iwt) - e^(-iwt)]. 2cos(wt) = [e^(iwt) + e^(-iwt)].
2sinh(wt) = [e^(-i(iwt)) - e^(i(iwt))] = [e^(wt) - e^(-wt)]= 2sin(-iwt)) = -2sin(iwt). 2cosh(wt) = (e^(-i(iwt)) + e^(i(iwt))) = (e^(wt) + e^(-wt)) = 2cos(iwt).
Further identities and such can be easier if
e^(iwt) = cos(wt) + isin(wt) is used instead of your noodle.
an aside I found interesting: e^(irwt) = cos(rwt) + isin(rwt) = (cos(wt) + isin(wt))^r. "polar notation". "(angle)" being that similar to "
Reply to
Simon Roberts
On 01/09/2017 23:41, Simon Roberts wrote:>
If you could but be patient while I work out what is 2 ohms, then I'll tell you in half a "mho".
Reply to
Gareth's Downstairs Computer

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