Prettty pleased with myself at finishing a pretty hard bit of coursework but am stuck on one single excercise.

I have calculated 3 voltages in sine waveform and now just need to verify that they are all the same frequency (w) The expressions for the voltages are

V1= 3sin(wt)
V2= 2cos(wt)
V3= 3.6sin(wt+0.588rad)

Pretty sure double and compound angle formulae are the way to go but I can’t find a way of applying it to get actual numbers back.

Probably just my brain being fried from too much studying, but a nudge in the right direction will be much appreciated

http://www.wolframalpha.com/input/?i=3sin%28wt%29+%3D+2cos%28wt%29

Forgot to mention V1+V2=V3
Good site that, cheers!

Wolfram Alpha is one site where it’s worth paying the pro fee IMHO.

http://www.wolframalpha.com/input/?i=3sin%28wt%29%2B2cos%28wt%29%3D3.6sin%28wt%2B0.588rad%29

I’m not sure how you prove this other than they all are!

If the coefficient of “t” is the same, the functions all have the same frequency and hence the same period!

edit: try looking up trigonometric wave function for further explanation

Using the compound angle formula and imposing the constant t at 1 allowed me to get to 3sinw+2cosw=3sinw+2cosw and therefore w=w. Pretty sure that’s proof enough

Erm they just ARE the same frequency, wt?

W=2pif

Same w same f

Our rearrange all of them for f and show they are equivalent

Well I got it marked as correct so all good! cheers all