# could someone please help me prove these equations have the same frequency

• Aug 13th 2012, 10:18 PM
rich1979
could someone please help me prove these equations have the same frequency
V1=3sin(wt)
V2=2cos(wt) v3=v1+v2
v3=3.61sin(wt+33.7degrees)

how do i prove that the resultant voltage V3 is in the same frequency as v1 and v2 ?
• Aug 13th 2012, 11:05 PM
Ranjan
Re: could someone please help me prove these equations have the same frequency
The frequency of v1 is w. The frequency of v2 is also w. It is a wave that has 2/3 of amplitude of v1 and phase shifted by 90deg. v3 has the same frequency w but its amplitude is 1.2 times that of v1 and phase shifted by 33.7 degrees. You can prove mathematically by expanding v3. Then you get a sine wave and a cosine wave with frequency w each. viz: v3=3.6sinwt.cos33.7+3.6coswt.sin33.7. You can write this as asinwt+bcoswt, where a and b are constants (the amplitudes). Hope this helps.
• Aug 13th 2012, 11:36 PM
Educated
Re: could someone please help me prove these equations have the same frequency
The general equation of a sine wave (and similarly, cosine wave) is $y = A \sin [B (x+C)] + D$
A affects amplitude
B affects frequency
C affects horizontal shift
D affects vertical shift

Do you see that the B value for all 3 of your equations is the same variable, therefore they must all have the same frequency.