I know this about this problem so far two waves one is sine and other is cosine wave we have to find the sum so V=v1+v2 v1 is a sine wave and has amplitude of 10 so i got the amplitude and they have given me the time period 2ms from here i can get frequency = 2π/T = 2π/2 = π in the second one its a cosine wave so again amplitude 10 and frequency is same but the the phase difference is 90 degree what angle does sine have it starts at zero so its angle is 0 ? and cosine 90 and after this
v1(t)=10sin(wt+θ)
v2(t)=10cost(wt+θ)

 

You need to write both waveforms as either sin() or cos(), not one of each.

 

I was asking am i right in writing the equation..is θ =0 and for cos θ= 90 and do i have to put the value of omega.
V1(t)=10cos(wt+Θ-90)
V2(t)=10cos(wt+90)
V(t)=10 /_-90degre + 10 /_0degre
changing to to rectangular form...and then solving for the v(t).

 

I was asking am i right in writing the equation..is θ =0 and for cos θ= 90 and do i have to put the value of omega.
V1(t)=10cos(wt+Θ-90)
V2(t)=10cos(wt+90)
V(t)=10 /_-90degre + 10 /_0degre
changing to to rectangular form...and then solving for the v(t).

In the problem statement, θ is the phase angle of the sum of the two signals.

What is Θ?

Going back to your original post, you started with these:

v1(t) = 10 sin(ωt+θ)
v2(t) = 10 cos(ωt+θ)

If v(t) is a voltage, then you need units. I can't tell from your diagram if it is a voltage or just a unitless math function, so I'll assume the latter.

Given the waveforms, what is θ equal to for these two waveforms?

The waveforms match the picture only for θ = 0, right?

So you have

v1(t) = 10 sin(ωt)
v2(t) = 10 cos(ωt)

Since the answer is supposed to be of the form v(t) = A·cos(ωt + θ), you need to write v1(t) and v2(t) in this form:

v1(t) = 10 sin(ωt) = 10 cos(ωt + φ)
v2(t) = 10 cos(ωt)

The question that needs to be answered (and that I think you are trying to ask) is what the value of φ needs to be.

Look at the diagram and focus on t=0. That means that you will have v1 = 10 cos(φ). At t=0, v1(t) = 0 and is rising as t increases. So ask yourself what the argument of cos() needs to be so that it is equal to zero and increases as the value of the argument increases.

 

You need to write both waveforms as either sin() or cos(), not one of each.

Sorry for not mentioning the units and thanks for your reply sorry for the symbol I accidentally put first sin signal is changed to cos and cos 90 is zero so angle would b 90 and amplitude is 10 ?
Do I have to add both ? because in the question they said that V(t)=v1(t)+v2(t)=Acos(wt+θ)
do I have to convert the v1(t)=10cos(wt+90)volts and v2(t)=10cos(wt)volts into phasor domain and add them in rectangular form...

 

If you are supposed to use phasors, then the phasors you use MUST be consistent -- so they must either both be based on sin() or both be based on cos().

If you don't have to use phasors, then you can just use a trig identity and be done.

 

Your awesome thanks for your time and for tolerating me thanks again