sin^2 in exponentials

[chorb]

I know the equation for sin(w) in exponentials (Euler's formula) is [e^(jw) - e^(-jw)]/2j but I want to know if there is a similar equation for sin^2(w) or for cos^2(w). Couldn't find anything googling it. where j = i = squareroot(-1).

This is only 1 step in my homework problem, which I am not even sure I am doing correctly but if an equation does exist then I think my method will work.

 

[TuxDave]

{[e^(jw) - e^(-jw)]/2j}^2 = sin^2(w)

 

[BrownTown]

meh, im taking a break from doing hours of EE homework and I come here to get away from it and here you are reming me of all the homework I have left 🙁 . Well, personally I don't know any of these by heart, Mathematica does all this crap for me, and if I ever do need to know the identites you can always look in the back of the book or google them. God help the person who has to do this type of work without Mathmatica,...I sure as hell couldn't do anything without it

 

[silverpig]

Isn't that for hyperbolic sine?

 

[chorb]

tuxdave you sure on that?

And ya this is for my EE class too. I cant seem to find any site or book that backs up what tuxdave says. For all i know it could or could not exist, thx for the info anyway.

 

[BrownTown]

i dunno, there like a billion different way to write these things, having no clue what you are working on it makes it hard to determine which one would work the best.

 

[CycloWizard]

Originally posted by: chorb
tuxdave you sure on that?

And ya this is for my EE class too. I cant seem to find any site or book that backs up what tuxdave says. For all i know it could or could not exist, thx for the info anyway.

Of course he's right. If x=y, then x^2=y^2.

 

[smack Down]

If you not sure you can do the proof of sin^2 + cos^2 = 1

 

[TuxDave]

Originally posted by: CycloWizard

Originally posted by: chorb
tuxdave you sure on that?

And ya this is for my EE class too. I cant seem to find any site or book that backs up what tuxdave says. For all i know it could or could not exist, thx for the info anyway.

Of course he's right. If x=y, then x^2=y^2.

Hehe... I thought what I did was an obvious display of laziness but I guess it didn't go through very well.

The other way to do it is to change sin^2(x) into something that has cos(2x) or sin(2x)... you know that identity and then use Euler on that.

 

[chorb]

ya tuxDave you were right, thanks, and thanks to all others who said the same thing. Im always hesitant to use common sense when doing math equations.